Publications
2023
- J. Mairal, J. Murillo, and P. GarcÃa-Navarro, "The entropy fix in augmented riemann solvers in presence of source terms: application to the shallow water equations," Computer methods in applied mechanics and engineering, vol. 417A, p. DOI: 10.1016/j.cma.2023.116411, 2023.
[Bibtex]@Article{mairal2023_01,AUTHOR = {Mairal, J. and Murillo, J. and Garc{\'i}a-Navarro, P.},TITLE = {The entropy fix in augmented Riemann solvers in presence of source terms: Application to the Shallow Water Equations},JOURNAL = {Computer Methods in Applied Mechanics and Engineering},VOLUME = {417A},YEAR = {2023},PAGES = {DOI: 10.1016/j.cma.2023.116411},} - J. Murillo and P. GarcÃa-Navarro, "Numerical coupling of 0d and 1d models in networks of vessels including transonic flow conditions. application to short-term transient and stationary hemodynamic simulation of postural changes," Int j numer meth biomedical engineering, p. doi:10.1002/cnm.3751, 2023.
[Bibtex]@Article{murillo2023_02,AUTHOR = {Murillo, J. and Garc{\'i}a-Navarro, P.},TITLE = {Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions.Application to short-term transient and stationary hemodynamic simulation of postural changes},JOURNAL = {Int J Numer Meth Biomedical Engineering},VOLUME = {},YEAR = {2023},PAGES = {doi:10.1002/cnm.3751},} - J. Fernández-Pato, S. MartÃnez-Aranda, and P. GarcÃa-Navarro, "A 2d hydraulic simulation model including dynamic piping and overtopping dambreach," Water, vol. 15(18), p. https://doi.org/10.3390/w15183268, 2023.
[Bibtex]@Article{jfpato2023_01,AUTHOR = {Fern{\'a}ndez-Pato, J. and Mart{\'i}nez-Aranda, S. and Garc{\'i}a-Navarro, P.},TITLE = {A 2D Hydraulic Simulation Model Including Dynamic Piping and Overtopping Dambreach},JOURNAL = {Water},VOLUME = {15(18)},YEAR = {2023},PAGES = {https://doi.org/10.3390/w15183268},} - D. Caviedes-Voullieme, M. Morales-Hernández, M. R. Norman, and I. Ozgen-Xian, "Serghei (serghei-swe) v1.0: a performance-portable high-performance parallel-computing shallow-water solver for hydrology and environmental hydraulics," Geosci. model dev., vol. 16, pp. 977-1008, 2023.
[Bibtex]@Article{cav2023_01,AUTHOR = {Caviedes-Voullieme, D. and Morales-Hern{\'a}ndez, M. and Norman, M. R. andOzgen-Xian, I.},TITLE = {SERGHEI (SERGHEI-SWE) v1.0: a performance-portable high-performance parallel-computing shallow-water solver for hydrologyand environmental hydraulics},JOURNAL = {Geosci. Model Dev.},VOLUME = {16},YEAR = {2023},PAGES = {977-1008},} - X. Li, D. Fu, J. Nielsen-Gammon, S. Gangrade, S. Kao, P. Chang, Z. Z. Mario Morales Hernández Nathalie Voisin, and H. Gao, "Impacts of climate change on future hurricane induced rainfall and flooding in a coastal watershed: a case study on hurricane harvey.," Journal of hydrology, vol. 616, p. 128774, 2023.
[Bibtex]@Article{mar2023_01,AUTHOR = {Xudong Li and Dan Fu and John Nielsen-Gammon and Sudershan Gangrade and Shih-Chieh Kao and Ping Chang and Mario Morales Hern{\'a}ndez, Nathalie Voisin, Zhe Zhang,and Huilin Gao},TITLE = {Impacts of climate change on future hurricane induced rainfall and flooding in a coastal watershed: a case study on HurricaneHarvey.},JOURNAL = {Journal of Hydrology},VOLUME = {616},YEAR = {2023},PAGES = {128774},} - P. Solán-Fustero, J. L. Gracia, Navas-Montilla A., and P. GarcÃa-Navarro, "Development of pod-based reduced order models applied to shallow water equations using augmented riemann solvers," Computer methods in applied mechanics and engineering, vol. 410, p. 116038, 2023.
[Bibtex]@Article{solan2023_01,AUTHOR = {Sol{\'a}n-Fustero, P. and Gracia, J. L. and Navas-Montilla, A., and Garc{\'i}a-Navarro, P.},TITLE = {Development of POD-based Reduced Order Models applied to shallow water equations using augmented Riemann solvers},JOURNAL = {Computer Methods in Applied Mechanics and Engineering},VOLUME = {410},YEAR = {2023},PAGES = {116038},} - S. MartÃnez-Aranda, J. Fernández-Pato, and P. GarcÃa-Navarro, "Non-equilibrium bedload transport model applied to erosive overtopping dambreach," Water, vol. 15(17), p. 3094, 2023.
[Bibtex]@Article{martinez2023_01,AUTHOR = {Mart{\'i}nez-Aranda, S. and Fern{\'a}ndez-Pato, J. and Garc{\'i}a-Navarro, P.},TITLE = {Non-Equilibrium Bedload Transport Model Applied to Erosive Overtopping Dambreach},JOURNAL = {Water},VOLUME = {15(17)},YEAR = {2023},PAGES = {3094},} - P. Vallés, I. Echeverribar, J. Mairal, S. MartÃnez-Aranda, J. Fernández-Pato, and P. GarcÃa-Navarro, "2d numerical simulation of floods in ebro river and analysis of strategies to model the mequinenza reservoir," Geohazards, vol. 1, pp. 1-23, 2023.
[Bibtex]@Article{valles2023_01,AUTHOR = {Vall\'es, Pablo and Echeverribar, Isabel and Mairal, Juan and Mart\'inez-Aranda, Sergio and Fern\'andez-Pato, Javier and Garc\'ia-Navarro, Pilar},TITLE = {2D numerical simulation of floods in Ebro River and analysis of strategies to model the Mequinenza Reservoir},JOURNAL = {Geohazards},VOLUME = {1},YEAR = {2023},PAGES = {1-23},} - I. Echeverribar, P. Brufau, and P. GarcÃa-Navarro, "Extension of a Roe-type Riemann solver scheme to model non-hydrostatic pressure shallow flows," Applied mathematics and computation, vol. 440, p. 127642, 2023.
[Bibtex]@Article{isa01,AUTHOR = {Echeverribar, I. and Brufau, P. and Garc\'ia-Navarro, P.},TITLE = {Extension of a {Roe-type Riemann} Solver Scheme to model Non-Hydrostatic Pressure Shallow Flows},JOURNAL = {Applied Mathematics and Computation},VOLUME = {440},YEAR = {2023},PAGES = {127642},} - I. Echeverribar, S. MartÃnez-Aranda, J. Fernández-Pato, and P. GarcÃa-Navarro, "A gpu-based 2d viscous flow model with variable density and heat exchange," Advances in engineering software, vol. 175, p. 103340, 2023.
[Bibtex]@Article{isa02,AUTHOR = {Echeverribar, I. and Mart\'inez-Aranda, S. and Fern\'andez-Pato, J. and Garc\'ia-Navarro, P.},TITLE = {A GPU-based 2D viscous flow model with variable density and heat exchange},JOURNAL = {Advances in Engineering Software},VOLUME = {175},YEAR = {2023},PAGES = {103340},}
2022
- S. MartÃnez-Aranda, J. Fernández-Pato, I. Echeverribar, A. Navas-Montilla, M. Morales-Hernández, P. Brufau, J. Murillo, and P. GarcÃa-Navarro, "Finite Volume models and Efficient Simulation Tools (EST) for shallow flows," in Advances in fluid mechanics: modelling and simulations, Springer nature, singapore. isbn:978-9-81191-437-9, 2022.
[Bibtex]@inbook{ESTchapter,author = {Mart{\'i}nez-Aranda, S. and Fern{\'a}ndez-Pato, J. and Echeverribar, I. and Navas-Montilla, A. and Morales-Hern{\'a}ndez, M. and Brufau, P. and Murillo, J. and Garc{\'i}a-Navarro, P.},title = {{F}inite {V}olume models and {E}fficient {S}imulation {T}ools ({EST}) for Shallow Flows},booktitle = {Advances in Fluid Mechanics: Modelling and Simulations},publisher = {Springer Nature, Singapore. ISBN:978-9-81191-437-9},year = {2022}} - S. MartÃnez-Aranda and P. GarcÃa-Navarro, "Efficient Simulation Tools (EST) sediment-laden for shallow flows," in Modeling of sediment transport, Intechopen limited, london. isbn: 978-1-80355-868-4, 2022.
[Bibtex]@inbook{chapter02,author = {Mart{\'i}nez-Aranda, S. and Garc{\'i}a-Navarro, P.},title = {{E}fficient {S}imulation {T}ools ({EST}) Sediment-Laden for Shallow Flows},booktitle = {Modeling of Sediment Transport},publisher = {IntechOpen Limited, London. ISBN: 978-1-80355-868-4},year = {2022}} - C. Juez and A. Navas-Montilla, "Numerical characterization of seiche waves energy potential in river bank lateral embayments," Renewable energy, vol. 186, pp. 143-156, 2022.
[Bibtex]@Article{adrian01,AUTHOR = {Juez, C. and Navas-Montilla, A.},TITLE = {Numerical characterization of seiche waves energy potential in river bank lateral embayments},JOURNAL = {Renewable Energy},VOLUME = {186},YEAR = {2022},PAGES = {143-156},} - P. Solán-Fustero, J. L. Gracia, A. Navas-Montilla, and P. Garc'ia-Navarro, "A pod-based rom strategy for the prediction in time of advection-dominated problems," Journal of computational physics, vol. 471, p. 111672, 2022.
[Bibtex]@Article{adrian03,AUTHOR = {Sol\'an-Fustero, P. and Gracia, J.L. and Navas-Montilla, A. and Garc'ia-Navarro, P.},TITLE = {A POD-based ROM strategy for the prediction in time of advection-dominated problems},JOURNAL = {Journal of Computational Physics},VOLUME = {471},YEAR = {2022},PAGES = {111672},} -
![[DOI]](https://ghc.unizar.es/wp-content/plugins/papercite/img/external.png)
R. Meurice, S. MartÃnez-Aranda, M. Ebrahimi, P. GarcÃa-Navarro, and S. Soares-Frazão, "Laser Profilometry to measure the bed evolution in a dam-break flow," Journal of hydraulic research, vol. (60), iss. 5, pp. 725-737, 2022.
[Bibtex]@article{sergioLaserProfile,author = {Meurice, R. and Mart{\'i}nez-Aranda, S. and Ebrahimi, M. and Garc{\'i}a-Navarro, P. and Soares-Fraz{\~a}o, S.},title = {{L}aser {P}rofilometry to measure the bed evolution in a dam-break flow},journal = {Journal of Hydraulic Research},volume = {(60)},number = {5},pages = {725-737},year = {2022},doi = {https://doi.org/10.1080/00221686.2022.2059584}} - S. MartÃnez-Aranda, J. Murillo, M. Morales-Hernández, and P. GarcÃa-Navarro, "Novel discretization strategies for the 2D non-Newtonian resistance term in geophysical shallow flows," Engineering geology, vol. 302, p. 106625, 2022.
[Bibtex]@article{sergio2Dresistance,author = {Mart{\'i}nez-Aranda, S. and Murillo, J. and Morales-Hern{\'a}ndez, M. and Garc{\'i}a-Navarro, P},title = {Novel discretization strategies for the {2D} non-{N}ewtonian resistance term in geophysical shallow flows},journal = {Engineering Geology},volume = {302},pages = {106625},year = {2022},doi = {https://doi.org/10.1016/j.enggeo.2022.106625}} - S. MartÃnez-Aranda, J. Murillo, and P. GarcÃa-Navarro, "A GPU-accelerated Efficient Simulation Tool (EST) for 2D variable-density mud/debris flows over non-uniform erodible beds," Engineering geology, vol. 296, p. 106462, 2022.
[Bibtex]@article{sergiomudflowGPU,author = {Mart{\'i}nez-Aranda, S. and Murillo, J. and Garc{\'i}a-Navarro, P},title = {A {GPU}-accelerated {E}fficient {S}imulation {T}ool ({EST}) for {2D} variable-density mud/debris flows over non-uniform erodible beds},journal = {Engineering Geology},volume = {296},pages = {106462},year = {2022},doi = {https://doi.org/10.1016/j.enggeo.2021.106462}} - P. Solán-Fustero, J. L. Gracia, A. Navas-Montilla, and P. GarcÃa-Navarro, "A POD-based ROM strategy for the prediction in time of advection-dominated problems," Journal of computational physics, vol. 471, p. 111672, 2022.
[Bibtex]@article{psolanfus01,author = {Sol{\'a}n-Fustero, P. and Gracia, J.L. and Navas-Montilla, A. and Garc{\'i}a-Navarro, P},title = {A {POD}-based {ROM} strategy for the prediction in time of advection-dominated problems},journal = {Journal of Computational Physics},volume = {471},pages = {111672},year = {2022},doi = {https://doi.org/10.1016/j.jcp.2022.111672}}
2021
- J. Murillo and P. GarcÃa-Navarro, "A solution of the junction riemann problem for 1d hyperbolic balance laws in networks including supersonic flow conditions on elastic collapsible tubes," Symmetry, vol. 13, iss. 9, 2021.
[Bibtex]@Article{sym13091658,AUTHOR = {Murillo, Javier and Garc\'ia-Navarro, Pilar},TITLE = {A Solution of the Junction Riemann Problem for 1D Hyperbolic Balance Laws in Networks including Supersonic Flow Conditions on Elastic Collapsible Tubes},JOURNAL = {Symmetry},VOLUME = {13},YEAR = {2021},NUMBER = {9},ARTICLE-NUMBER = {1658},URL = {https://www.mdpi.com/2073-8994/13/9/1658},ISSN = {2073-8994},ABSTRACT = {The numerical modeling of one-dimensional (1D) domains joined by symmetric or asymmetric bifurcations or arbitrary junctions is still a challenge in the context of hyperbolic balance laws with application to flow in pipes, open channels or blood vessels, among others. The formulation of the Junction Riemann Problem (JRP) under subsonic conditions in 1D flow is clearly defined and solved by current methods, but they fail when sonic or supersonic conditions appear. Formulations coupling the 1D model for the vessels or pipes with other container-like formulations for junctions have been presented, requiring extra information such as assumed bulk mechanical properties and geometrical properties or the extension to more dimensions. To the best of our knowledge, in this work, the JRP is solved for the first time allowing solutions for all types of transitions and for any number of vessels, without requiring the definition of any extra information. The resulting JRP solver is theoretically well-founded, robust and simple, and returns the evolving state for the conserved variables in all vessels, allowing the use of any numerical method in the resolution of the inner cells used for the space-discretization of the vessels. The methodology of the proposed solver is presented in detail. The JRP solver is directly applicable if energy losses at the junctions are defined. Straightforward extension to other 1D hyperbolic flows can be performed.},DOI = {10.3390/sym13091658}} - P. Echeverribar, P. Vallés, J. Mairal, and P. GarcÃa-Navarro, "Efficient reservoir modelling for flood regulation in the ebro river (spain)," Water, vol. 12, p. 3160, 2021.
[Bibtex]@Article{isa03,AUTHOR = {Echeverribar, P. and Vall\'es, P. and Mairal, J. and Garc\'ia-Navarro, P.},TITLE = {Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain)},JOURNAL = {Water},VOLUME = {12},YEAR = {2021},PAGES = {3160},} - M. Morales-Hernández, M. B. Sharif, A. Kalyanapu, S. K. Ghafoor, T.T.Dullo, S. Gangrade, S. -C. Kao, M. R. Norman, and K. J. Evans, "TRITON: a Multi-GPU open source 2D hydrodynamic flood model," Environmental modelling and software, vol. 141, p. 105034, 2021.
[Bibtex]@article{mario01,author = {M. Morales-Hern\'andez and Md B. Sharif and A. Kalyanapu and S.K. Ghafoor and T.T.Dullo and S. Gangrade and S.-C. Kao and M.R. Norman and K.J. Evans},title = {{TRITON}: A {M}ulti-{GPU} open source {2D} hydrodynamic flood model},journal = {Environmental Modelling and Software},volume = {141},pages = {105034},year = {2021},doi = {https://doi.org/10.1016/j.envsoft.2021.105034}} - X. Li, C. Rankin, S. Gangrade, G. Zhao, K. Lander, N. Voisin, M. Shao, M. Morales-Hernández, S. Kao, and H. Gao, "Evaluating precipitation, streamflow, and inundation forecasting skills during extreme weather events: A case study for an urban watershed," Journal of hydrology, vol. 603(Part D), p. 127126, 2021.
[Bibtex]@article{mario02,author = {Xudong Li and Cheryl Rankin and Sudershan Gangrade and Gang Zhao and Kris Lander and Nathalie Voisin and Manqing Shao and Mario Morales-Hern\'andez and Shih-Chieh Kao andHuilin Gao},title = {Evaluating precipitation, streamflow, and inundation forecasting skills during extreme weather events: {A} case study for an urban watershed},journal = {Journal of Hydrology},volume = {603(Part D)},pages = {127126},year = {2021},doi = {https://doi.org/10.1016/j.jhydrol.2021.127126}} - T. T. Dullo, G. K. Darkwah, S. Gangrade, M. Morales-Hernández, M. B. Sharif, A. J. Kalyanapu, S. -C. Kao, S. Ghafoor, and M. and Ashfaq, "Assessing climate-change-induced flood risk in the Conasauga River watershed: an application of ensemble hydrodynamic inundation modeling," Nat. hazards earth syst., vol. 21, pp. 1739-1757, 2021.
[Bibtex]@article{mario03,author = {Dullo, T. T. and Darkwah, G. K. and Gangrade, S. and Morales-Hern\'andez, M. and Sharif, M. B. and Kalyanapu, A. J. and Kao, S.-C. and Ghafoor, S. and and Ashfaq, M.},title = {Assessing climate-change-induced flood risk in the {C}onasauga {R}iver watershed: an application of ensemble hydrodynamic inundation modeling},journal = {Nat. Hazards Earth Syst.},volume = {21},pages = {1739-1757},year = {2021},doi = {https://doi.org/10.5194/nhess-21-1739-2021}} - G. Gordillo, M. Morales-Hernández, and P. GarcÃa-Navarro, "Transport control at channel junctions using adjoint sensitivity," Mathematics, vol. 10, p. 93, 2021.
[Bibtex]@article{mario04,author = {Gordillo, G. and Morales-Hern\'andez, M. and Garc\'ia-Navarro, P.},title = {Transport Control at Channel Junctions Using Adjoint Sensitivity},journal = {Mathematics },volume = {10},pages = {93},year = {2021},doi = {https://doi.org/10.3390/math10010093}} - J. Fernández-Pato and P. GarcÃa-Navarro, "An efficient GPU implementation of a coupled overland-sewer hydraulic model with pollutant transport," Hydrology, vol. 8(4), p. 146, 2021.
[Bibtex]@article{FernandezPato2021,title = {An efficient {GPU} implementation of a coupled overland-sewer hydraulic model with pollutant transport},journal = {Hydrology},volume = {8(4)},pages = {146},year = {2021},doi = {doi.org/10.3390/hydrology8040146},author = {Fern{\'a}ndez-Pato, J. and Garc{\'i}a-Navarro, P.},abstract = {Numerical simulation of flows that consider interaction between overland and drainage networks has become a practical tool to prevent and mitigate flood situations in urban environments, especially when dealingwith intense storm events, where the limited capacity of the sewer systems can be a trigger for flooding. Additionally, in order to prevent any kind of pollutant dispersion through the drainage network, it is very interestingto have a certain monitorization or control over the quality of the water that flows in both domains. In this sense, the addition of a pollutant transport component to both surface and sewer hydraulic models would benefit theglobal analysis of the combined water flow. On the other hand, when considering a realistic large domain with complex topography or streets structure, a fine spatial discretization is mandatory. Hence the number of grid cellsis usually very large and, therefore, it is necessary to use parallelization techniques for the calculation, the use of Graphic Processing Units (GPU) being one of the most efficient due to the leveraging of thousands of processorswithin a single device. In this work, an efficient GPU-based 2D shallow water flow solver (RiverFlow2D-GPU) is fully coupled with EPA’s Storm Water Management Model (SWMM). Both models are able to develop a transient water qualityanalysis taking into account several pollutants. The coupled model, referred to as RiverFlow2D-GPU UD (Urban Drainge) is applied to three real-world cases, covering the most common hydraulic situations in urban hydrology/hydraulics.A UK Environmental Agency test case is used as model validation, showing a good agreement between RiverFlow2D-GPU UD and the rest of the numerical models considered. The efficiency of the model is proven in two more complex domains,leading to a >100x faster simulations compared with the traditional CPU computation.},} - M. Morales-Hernández, M. B. Sharif, A. Kalyanapu, S. K. Ghafoor, T. T. Dullo, S. Gangrade, S. -C. Kao, M. R. Norman, and K. J. Evans, "TRITON: a multi-GPU open source 2D hydrodynamic flood model," Environmental modelling & software, vol. 141, p. 105034, 2021.
[Bibtex]@article{morales2021c,title = {{TRITON}: A Multi-{GPU} open source {2D} hydrodynamic flood model},journal = {Environmental Modelling & Software},volume = {141},pages = {105034},year = {2021},issn = {1364-8152},doi = {10.1016/j.envsoft.2021.105034},author = {M. Morales-Hern{\'a}ndez and Md B. Sharif and A. Kalyanapu and S.K. Ghafoor and T.T. Dullo and S. Gangrade and S.-C. Kao and M.R. Norman and K.J. Evans},} - P. Solán-Fustero, A. Navas-Montilla, E. Ferrer, J. Manzanero, and P. GarcÃa-Navarro, "Application of approximate dispersion-diffusion analyses to under-resolved burgers turbulence using high resolution WENO and UWC schemes," Journal of computational physics, vol. 435, p. 110246, 2021.
[Bibtex]@article{spectral_analysis,author = {P. Sol{\'a}n-Fustero and A. Navas-Montilla and E. Ferrer and J. Manzanero and P. Garc{\'i}a-Navarro},title = {Application of approximate dispersion-diffusion analyses to under-resolved Burgers turbulence using high resolution {WENO} and {UWC} schemes},journal = {Journal of Computational Physics},volume = {435},pages = {110246},year = {2021},doi = {10.1016/j.jcp.2021.110246},} - T. T. Dullo, G. K. Darkwah, S. Gangrade, M. Morales-Hernández, B. M. Sharif, A. J. Kalyanapu, S. Kao, S. Ghafoor, and M. Ashfaq, "Assessing climate-change-induced flood risk in the conasauga river watershed: an application of ensemble hydrodynamic inundation modeling," , vol. 21, iss. 6, 2021.
[Bibtex]@article{morale2021b,title = {Assessing climate-change-induced flood risk in the Conasauga River watershed: an application of ensemble hydrodynamic inundation modeling},author = {Dullo, Tigstu T. and Darkwah, George K. and Gangrade, Sudershan and Morales-Hern{\'a}ndez, Mario and Sharif, M. Bulbul and Kalyanapu, Alfred J. and Kao, Shih-Chieh and Ghafoor, Sheikh and Ashfaq, Moetasim},number = {6},volume = {21},year = {2021},doi = {10.5194/nhess-21-1739-2021},} - S. MartÃnez-Aranda, R. Meurice, S. Soares-Frazão, and P. GarcÃa-Navarro, "Comparative analysis of HLLC- and Roe-based models for the simulation of a dambreak flow in an erodible channel with a 90 bend," Water, vol. 13, p. 1840, 2021.
[Bibtex]@article{bedload_nonCapacity,author = {Mart{\'i}nez-Aranda, S. and Meurice, R. and Soares-Fraz{\~a}o, S. and Garc{\'i}a-Navarro, P.},title = {Comparative analysis of {HLLC-} and {R}oe-based models for the simulation of a dambreak flow in an erodible channel with a 90 bend},journal = {Water},volume = {13},number = {},pages = {1840},year = {2021},doi = {10.3390/w13131840}} - I. Özgen-Xian, A. Navas-Montilla, D. Dwivedi, and S. Molins, "Hyperbolic reformulation approach to enable efficient simulation of groundwater flow and reactive transport," Environmental engineering science, vol. 38, iss. 3, pp. 181-191, 2021.
[Bibtex]@article{navasmontilla2021a,author = {{\"O}zgen-Xian, Ilhan and Navas-Montilla, Adrian and Dwivedi, Dipankar and Molins, Sergi},title = {Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport},journal = {Environmental Engineering Science},volume = {38},number = {3},pages = {181-191},year = {2021},doi = {10.1089/ees.2020.0363},} - S. MartÃnez-Aranda, J. Murillo, and P. GarcÃa-Navarro, "Comparison of new efficient 2D models for the simulation of bedload transport using the augmented Roe approach," Advances in water resources, vol. 153, p. 103931, 2021.
[Bibtex]@article{bedload_fully_coupled,author = {Mart{\'i}nez-Aranda, S. and Murillo, J. and Garc{\'i}a-Navarro, P.},title = {Comparison of new efficient {2D} models for the simulation of bedload transport using the augmented {R}oe approach},journal = {Advances in Water Resources},volume = {153},number = {},pages = {103931},year = {2021},doi = {10.1016/j.advwatres.2021.103931}} - T. T. Dullo, S. Gangrade, M. Morales-Hernández, M. B. Sharif, S. Kao, A. J. Kalyanapu, S. Ghafoor, and K. J. Evans, "Simulation of hurricane harvey flood event through coupled hydrologic-hydraulic models: challenges and next steps," Journal of flood risk management, vol. n/a, p. e12716, 2021.
[Bibtex]@article{morales2021a,author = {Dullo, Tigstu T. and Gangrade, Sudershan and Morales-Hern{\'a}ndez, Mario and Sharif, Md Bulbul and Kao, Shih-Chieh and Kalyanapu, Alfred J. and Ghafoor, Sheikh and Evans, Katherine J.},title = {Simulation of Hurricane Harvey flood event through coupled hydrologic-hydraulic models: Challenges and next steps},journal = {Journal of Flood Risk Management},volume = {n/a},pages = {e12716},year = {2021},doi = {10.1111/jfr3.12716},} - A. Navas-Montilla, S. MartÃnez-Aranda, A. Lozano, I. GarcÃa-PalacÃn, and P. GarcÃa-Navarro, "2D experiments and numerical simulation of the oscillatory shallow flow in an open channel lateral cavity," Advances in water resources, vol. 148, p. 103836, 2021.
[Bibtex]@article{kinect_cavity,author = {Navas-Montilla, A. and Mart{\'i}nez-Aranda, S. and Lozano, A. and Garc{\'i}a-Palac{\'i}n, I. and Garc{\'i}a-Navarro, P.},title = {{2D} experiments and numerical simulation of the oscillatory shallow flow in an open channel lateral cavity},journal = {Advances in Water Resources},volume = {148},number = {},pages = {103836},year = {2021},doi = {10.1016/j.advwatres.2020.103836}}
2020
- M. B. Sharif, S. K. Ghafoor, T. M. Hines, M. Morales-Hernández, K. J. Evans, S. Kao, A. J. Kalyanapu, T. T. Dullo, and S. Gangrade, "Performance evaluation of a two-dimensional flood model on heterogeneous high-performance computing architectures," in Proceedings of the platform for advanced scientific computing conference, Association for computing machinery, 2020.
[Bibtex]@inbook{10.1145/3394277.3401852,author = {Sharif, Md Bulbul and Ghafoor, Sheikh K. and Hines, Thomas M. and Morales-Hern{\'a}ndez, Mario and Evans, Katherine J. and Kao, Shih-Chieh and Kalyanapu, Alfred J. and Dullo, Tigstu T. and Gangrade, Sudershan},title = {Performance Evaluation of a Two-Dimensional Flood Model on Heterogeneous High-Performance Computing Architectures},booktitle = {Proceedings of the Platform for Advanced Scientific Computing Conference},year = {2020},publisher = {Association for Computing Machinery},doi = {10.1145/3394277.3401852},} - M. Morales-Hernández, M. B. Sharif, S. Gangrade, T. T. Dullo, S. -C. Kao, A. Kalyanapu, S. K. Ghafoor, K. J. Evans, E. Madadi-Kandjani, and B. R. Hodges, "High-performance computing in water resources hydrodynamics," Journal of hydroinformatics, vol. 22, iss. 5, pp. 1217-1235, 2020.
[Bibtex]@article{10.2166/hydro.2020.163,author = {Morales-Hern{\'a}ndez, M. and Sharif, M. B. and Gangrade, S. and Dullo, T. T. and Kao, S.-C. and Kalyanapu, A. and Ghafoor, S. K. and Evans, K. J. and Madadi-Kandjani, E. and Hodges, B. R.},title = "{High-performance computing in water resources hydrodynamics}",journal = {Journal of Hydroinformatics},volume = {22},number = {5},pages = {1217-1235},year = {2020},doi = {10.2166/hydro.2020.163},} - G. Gordillo, M. Morales-Hernández, I. Echeverribar, J. Fernández-Pato, and P. GarcÃa-Navarro, "A GPU-based 2D shallow water quality model," Journal of hydroinformatics, vol. 22(5), pp. 1182-1197, 2020.
[Bibtex]@article{waterquality,title = "A {GPU}-based {2D} Shallow Water quality model",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1182-1197",year = "2020",author = "G. Gordillo and M. Morales-Hern{\'a}ndez and I. Echeverribar and J. Fern{\'a}ndez-Pato and P. Garc{\'i}a-Navarro",} - J. Fernández-Pato, S. MartÃnez-Aranda, M. Morales-Hernández, and P. GarcÃa-Navarro, "Analysis of the performance of different culvert boundary conditions in 2D shallow flow models," Journal of hydroinformatics, vol. 22(5), pp. 1093-1121, 2020.
[Bibtex]@article{FERNANDEZPATO2020b,title = "Analysis of the performance of different culvert boundary conditions in {2D} shallow flow models",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1093-1121",year = "2020",author = "J. Fern{\'a}ndez-Pato and S. Mart{\'i}nez-Aranda and M. Morales-Hern{\'a}ndez and P. Garc{\'i}a-Navarro",doi={10.2166/hydro.2020.025}} - G. Gordillo, M. Morales-Hernández, and P. GarcÃa-Navarro, "A gradient-descent adjoint method for the reconstruction of boundary conditions in a river flow nitrification model," Environmental Science: Processes & Impacts, vol. 22, pp. 381-397, 2020.
[Bibtex]@article{geovanny01,title = "A gradient-descent adjoint method for the reconstruction of boundary conditions in a river flow nitrification model",journal = "Environmental {S}cience: {P}rocesses \& {I}mpacts",volume = "22",pages = "381-397",year = "2020",author = "G. Gordillo and M. Morales-Hern{\'a}ndez and P. Garc{\'i}a-Navarro",} - A. Navas-Montilla, S. P. ', J. Murillo, and P. GarcÃa-Navarro, "Discontinuous galerkin well-balanced schemes using augmented riemann solvers with application to the shallow water equations," Journal of hydroinformatics, vol. 22(5), pp. 1038-1058, 2020.
[Bibtex]@article{navas2020a,title = "Discontinuous Galerkin well-balanced schemes using augmented Riemann solvers with application to the shallow water equations",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1038-1058",year = "2020",author = "A. Navas-Montilla and P. Sol{\'}n-Fustero and J. Murillo and P. Garc{\'i}a-Navarro",} - J. Murillo, S. MartÃnez-Aranda, A. Navas-Montilla, and P. GarcÃa-Navarro, "Adaptation of flux-based solvers to 2d two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts," Journal of hydroinformatics, vol. 22(5), pp. 972-1014, 2020.
[Bibtex]@article{murillo2020c,title = "Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "972-1014",year = "2020",author = "J. Murillo and S. Mart{\'i}nez-Aranda and A. Navas-Montilla and P. Garc{\'i}a-Navarro",doi={10.2166/hydro.2020.207}} - S. MartÃnez-Aranda, A. Ramos-Pérez, and P. GarcÃa-Navarro, "A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet-dry treatment," Journal of hydroinformatics, vol. 22(5), pp. 1015-1037, 2020.
[Bibtex]@article{martinez2020b,title = "A {1D} shallow-flow model for two-layer flows based on {FORCE} scheme with wet-dry treatment",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1015-1037",year = "2020",author = "S. Mart{\'i}nez-Aranda and A. Ramos-P{\'e}rez and P. Garc{\'i}a-Navarro",doi={10.2166/hydro.2020.002}} - S. MartÃnez-Aranda, J. Murillo, and P. GarcÃa-Navarro, "A robust two-dimensional model for highly sediment-laden unsteady flows of variable density over movable beds," Journal of hydroinformatics, vol. 22(5), pp. 1038-1060, 2020.
[Bibtex]@article{martinez2020a,title = "A robust two-dimensional model for highly sediment-laden unsteady flows of variable density over movable beds",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1038-1060",year = "2020",author = "S. Mart{\'i}nez-Aranda and J. Murillo and P. Garc{\'i}a-Navarro",doi={10.2166/hydro.2020.027}} - I. Echeverribar, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "Analysis of the performance of a hybrid CPU/GPU 1D2D coupled model for real flood cases," Journal of hydroinformatics, vol. 22(5), pp. 1198-1216, 2020.
[Bibtex]@article{echeverribar2020a,title = "Analysis of the performance of a hybrid {CPU}/{GPU} {1D2D} coupled model for real flood cases",journal = "Journal of Hydroinformatics",volume = "22(5)",pages = "1198-1216",year = "2020",author = "I. Echeverribar and M. Morales-Hern{\'a}ndez and P. Brufau and P. Garc{\'i}a-Navarro",} - J. Fernández-Pato, S. MartÃnez-Aranda, and P. GarcÃa-Navarro, "A 2D finite volume simulation tool to enable the assessment of combined hydrological and morphodynamical processes in mountain catchments," Advances in water resources, vol. 141, p. 103617, 2020.
[Bibtex]@article{FERNANDEZPATO2020103617,title = "A {2D} finite volume simulation tool to enable the assessment of combined hydrological and morphodynamical processes in mountain catchments",journal = "Advances in Water Resources",volume = "141",pages = "103617",year = "2020",issn = "0309-1708",doi = "https://doi.org/10.1016/j.advwatres.2020.103617",url = "http://www.sciencedirect.com/science/article/pii/S0309170819308334",author = "J. Fernández-Pato and S. MartÃnez-Aranda and P. GarcÃa-Navarro",keywords = "Shallow flows, Groundwater flow, Sediment transport, Infiltration, Coupled models",abstract = "Nowadays, the great power of modern computers allows to develop computational models able to deal with simulations of several coupled phenomena over detailed complex topography. An efficient and properly calibrated computational model represents a useful tool to provide insight into the catchment dynamics at hydrological and geomorphological levels. In addition, it allows to develop detailed risk management and conservation plans. In this work, we present a coupled surface-groundwater distributed flow model with hydrological (rainfall and infiltration) and geomorphological (suspended and bed load sediment transport) components. The coupled model is applied to well characterized experimental catchments that are used as realistic test cases. The calibration of the water flow model response to rainfall is performed by means of the fitting to experimental outlet hydrographs of the results supplied by a coupled formulation of 2D Shallow Water Equations and 2D Darcy’s law for saturated porous media connected via suitable infiltration laws. The calibration of a suspended and bed load model is also addressed by means of the fitting to experimental outlet sedigraphs. The numerical results show a good agreement between numerical and observed hydrographs and sedigraphs, significantly improving previous published simulations. Additionally, the need to repeat the simulations in the calibration processes is no longer an unapproachable problem."} - D. Caviedes-Voullième, J. Fernández-Pato, and C. Hinz, "Performance assessment of 2d zero-inertia and shallow water models for simulating rainfall-runoff processes," Journal of hydrology, vol. 584, p. 124663, 2020.
[Bibtex]@article{CAVIEDESVOULLIEME2020124663,title = "Performance assessment of 2D Zero-Inertia and Shallow Water models for simulating rainfall-runoff processes",journal = "Journal of Hydrology",volume = "584",pages = "124663",year = "2020",issn = "0022-1694",doi = "https://doi.org/10.1016/j.jhydrol.2020.124663",url = "http://www.sciencedirect.com/science/article/pii/S0022169420301232",author = "Daniel Caviedes-Voullième and Javier Fernández-Pato and Christoph Hinz",keywords = "Surface runoff, Runoff generation, Pluvial flooding, Zero-inertia equation, Shallow-water equations, Diffusive-wave equation",abstract = "Rainfall-runoff simulations are increasingly being performed with physically-based and spatially distributed solvers. The current computational and numerical technology enables the use of full shallow water equations solvers to be applied for these type of flow problems. Nonetheless, Zero-Inertia (diffusive wave) solvers have been historically favoured due to their conceptual and mathematical simplicity in comparison to shallow water solvers, with the working assumption that the simplifications introduced by Zero-Inertia will have some assumable impact on accuracy but will also allow for computational efficiency. Since both types of solvers have been primarily developed, benchmarked and compared to each other for fluvial and floodplain simulations, it is relevant to assess t-he relative performance for rainfall-runoff problems. In this work, both solvers are applied to a set of six well known test cases with reference solutions. The performance of the solvers is assessed in terms of global signatures such as hydrographs and flooded areas, but also in terms of spatial distributions of depth and velocity, as well as computational cost. Furthermore, the comparisons are performed across different spatial resolutions. The results show that for rainfall-runoff problems explicit, finite volumes solvers for both equations provide a similar accuracy, but the shallow water solver requires less computational time. The Zero-Inertia solver was found to be less sensitive to mesh refining than the full shallow water solver."} - G. Bertaglia, A. Navas-Montilla, A. Valiani, M. I. M. GarcÃa, J. Murillo, and V. Caleffi, "Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data," Journal of biomechanics, vol. 100, p. 109595, 2020.
[Bibtex]@article{navas2020b,title = "Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data",journal = "Journal of Biomechanics",volume = "100",pages = "109595",year = "2020",author = "G. Bertaglia, and A. Navas-Montilla and A. Valiani and M.I.M. GarcÃa and J. Murillo and V. Caleffi",} - A. Navas-Montilla and C. Juez, "Numerical ability of hyperbolic flux solvers to compute 2d shear layers in turbulent shallow flows," Advances in water resources, vol. 135, p. 103482, 2020.
[Bibtex]@article{navas2020c,title = "Numerical ability of hyperbolic flux solvers to compute 2D shear layers in turbulent shallow flows",journal = "Advances in Water Resources",volume = "135",pages = "103482",year = "2020",author = "A. Navas-Montilla and C. Juez",} - G. Gordillo, M. Morales-Hernández, and P. GarcÃa-Navarro, "Finite volume model for the simulation of 1D unsteady river flow and water quality based on the WASP," Journal of Hydroinformatics, vol. 22(2), pp. 327-345, 2020.
[Bibtex]@article{10.2166/hydro.2019.080,author = {Gordillo, Geovanny and Morales-Hernández, Mario and GarcÃa-Navarro, Pilar},title = "{Finite volume model for the simulation of 1D unsteady river flow and water quality based on the WASP}",journal = {Journal of {H}ydroinformatics},year = {2020},volume = "22(2)",pages = "327-345",doi = {10.2166/hydro.2019.080},url = {https://doi.org/10.2166/hydro.2019.080},}
2019
- S. MartÃnez-Aranda, J. Murillo, and P. GarcÃa-Navarro, "A comparative analysis of capacity and non-capacity formulations for the simulation of unsteady flows over finite-depth erodible beds," Advances in water resources, vol. 130, pp. 91-112, 2019.
[Bibtex]@article{MARTINEZARANDA201991,title = "A comparative analysis of capacity and non-capacity formulations for the simulation of unsteady flows over finite-depth erodible beds",journal = "Advances in Water Resources",volume = "130",pages = "91 - 112",year = "2019",issn = "0309-1708",doi = "https://doi.org/10.1016/j.advwatres.2019.06.001",url = "http://www.sciencedirect.com/science/article/pii/S0309170819302453",author = "S. Mart{\'i}nez-Aranda and J. Murillo and P. Garc{\'i}a-Navarro",} - J. Fernández-Pato, A. Sánchez, and P. GarcÃa-Navarro, "Simulación de avenidas mediante un modelo hidráulico/hidrológico distribuido en un tramo urbano del rÃo Ginel (Fuentes de Ebro)," Ribagua, vol. 6, iss. 1, pp. 49-62, 2019.
[Bibtex]@article{FernandezPato2019b,title = "Simulación de avenidas mediante un modelo hidráulico/hidrológico distribuido en un tramo urbano del rÃo {G}inel ({F}uentes de {E}bro)",journal = "Ribagua",volume = "6",number = "1",pages = "49-62",year = "2019",author = "Fern{\'a}ndez-Pato, J. and S\'{a}nchez, A. and Garc{\'i}a-Navarro, P.",doi = {10.1080/23863781.2019.1622473},url = {http://www.sciencedirect.com/science/article/pii/S0045793019301185},} - A. Navas-Montilla, J. Murillo, and P. GarcÃa-Navarro, "Modelos de simulación de alto orden para la resolución de fenómenos de propagación de ondas en flujos de lámina libre con turbulencia," IngenierÃa del agua, vol. 23, iss. 4, pp. 275-287, 2019.
[Bibtex]@article{10.4995/ia.2019.12169,author = {Navas-Montilla, A. and Murillo, J. and GarcÃa-Navarro, P.},title = "{Modelos de simulación de alto orden para la resolución de fenómenos de propagación de ondas en flujos de lámina libre con turbulencia}",journal = {IngenierÃa del agua},volume = {23},number = {4},pages = {275-287},year = {2019},month = {10},abstract = "{En este trabajo se presenta una herramienta de simulación basada en la resolución transitoria de grandes remolinos (URANS o DA-LES) para flujos turbulentos de aguas poco profundas en los que la turbulencia es predominantemente horizontal. El aspecto fundamental del modelo es la combinación de una discretización de alto orden en espacio y tiempo con una modelización de los efectos en el flujo promedio de las escalas turbulentas no resueltas. El modelo propuesto garantiza con precisión de máquina el equilibrio hidrostático (propiedad well-balanced) gracias a la utilización de una formulación del flujo numérico que incluye los términos fuente en la resolución del problema de Riemann derivativo en las paredes de las celdas. Se presenta una validación del modelo utilizando datos de literatura para un experimento de laboratorio que involucra un flujo de aguas poco profundas sobre una isla cónica, que da lugar a la generación de una calle de vórtices aguas abajo de la isla. Los resultados numéricos muestran que el modelo propuesto es capaz de reproducir fenómenos turbulentos bidimensionales, proporcionando un mayor nivel de detalle que la aproximación RANS tradicional.}",issn = {1134-2196},doi = {10.4995/ia.2019.12169},url = {https://doi.org/10.4995/ia.2019.12169},eprint = {https://iwaponline.com/IA/article-pdf/23/4/275/622474/ia201912169.pdf},} - G. Bertaglia, A. Navas-Montilla, A. Valiani, M. I. M. GarcÃa, J. Murillo, and V. Caleffi, "Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data," Journal of biomechanics, p. 109595, 2019.
[Bibtex]@article{BERTAGLIA2019109595,title = "Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data",journal = "Journal of Biomechanics",pages = "109595",year = "2019",issn = "0021-9290",doi = "https://doi.org/10.1016/j.jbiomech.2019.109595",url = "http://www.sciencedirect.com/science/article/pii/S0021929019308589",author = "Giulia Bertaglia and Adrián Navas-Montilla and Alessandro Valiani and Manuel Ignacio Monge GarcÃa and Javier Murillo and Valerio Caleffi",} - J. Murillo, A. Navas-Montilla, and P. GarcÃa-Navarro, "Formulation of exactly balanced solvers for blood flow in elastic vessels and their application to collapsed states," Computers & Fluids, vol. 186, pp. 74-98, 2019.
[Bibtex]@article{MURILLO201974,title = "Formulation of exactly balanced solvers for blood flow in elastic vessels and their application to collapsed states",journal = "Computers & {F}luids",volume = "186",pages = "74 - 98",year = "2019",issn = "0045-7930",doi = "https://doi.org/10.1016/j.compfluid.2019.04.008",url = "http://www.sciencedirect.com/science/article/pii/S0045793019301185",author = "J. Murillo and A. Navas-Montilla and P. GarcÃa-Navarro",keywords = "ARoe, HLLS, Positivity preserving, Flow limitation, Extreme collapse, Stability",abstract = "In this work, numerical solvers based on extensions of the Roe and HLL schemes are adapted to deal with test cases involving extreme collapsing conditions in elastic vessels. To achieve this goal, the system is transformed to provide a conservation–law form, allowing to define Rankine–Hugoniot conditions. The approximate solvers allow to describe the inner states of the solution. Therefore, source term fixes can be used to prevent unphysical values of vessel area and, at the same time, the eigenvalues of the system control stability. Numerical solvers of different order are tested using a wide variety of Riemann problems, including extreme vessel collapse and blockage. In all cases, the robustness of the approximate solvers presented here is checked using first and third order methods in time and space, using the WENO reconstruction scheme in combination with the TVDRK3 method."} - I. Echeverribar, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "2D numerical simulation of unsteady flows for large scale floods prediction in real time," Advances in water resources, vol. 134, p. 103444, 2019.
[Bibtex]@article{ECHEVERRIBAR2019103444,title = "{2D} numerical simulation of unsteady flows for large scale floods prediction in real time",journal = "Advances in Water Resources",volume = "134",pages = "103444",year = "2019",issn = "0309-1708",doi = "https://doi.org/10.1016/j.advwatres.2019.103444",url = "http://www.sciencedirect.com/science/article/pii/S0309170819304786",author = "I. Echeverribar and M. Morales-Hernández and P. Brufau and P. GarcÃa-Navarro",keywords = "Computational mesh, Shallow water flow, GPU, Real time flood prediction",abstract = "The challenge of finding a compromise between computational time and level of accuracy and robustness has traditionally expanded the use simplified models rather than full two-dimensional (2D) models for flood simulation. This work presents a GPU accelerated 2D shallow water model for the simulation of flood events in real time. In particular, an explicit first-order finite volume scheme is detailed to control the numerical instabilities that are likely to appear when used in complex topography. The model is first validated with the benchmark test case of the Toce River (Italy) and numerical fixes are demonstrated to be necessary. The model is next applied to reproduce real events in a reach of the Ebro River (Spain) in order to compare simulation results with field data. The second case deals with a large domain (744 km2) and long flood duration (up to 20 days) allowing an analysis of the performance and speed-up achieved by different GPU devices. The high values of fit between observed and simulated results as well as the computational times achieved are encouraging to propose the use of the model as forecasting system."} - P. GarcÃa-Navarro, J. Murillo, J. Fernández-Pato, I. Echeverribar, and M. Morales-Hernández, "The shallow water equations and their application to realistic cases," Environmental fluid mechanics, 2019.
[Bibtex]@Article{GarcÃa-Navarro2019,author="Garc{\'i}a-Navarro, P.and Murillo, J.and Fern{\'a}ndez-Pato, J.and Echeverribar, I.and Morales-Hern{\'a}ndez, M.",title="The shallow water equations and their application to realistic cases",journal="Environmental Fluid Mechanics",year="2019",month="Jan",day="05",abstract="The numerical modelling of 2D shallow flows in complex geometries involving transient flow and movable boundaries has been a challenge for researchers in recent years. There is a wide range of physical situations of environmental interest, such as flow in open channels and rivers, tsunami and flood modelling, that can be mathematically represented by first-order non-linear systems of partial differential equations, whose derivation involves an assumption of the shallow water type. Shallow water models may include more sophisticated terms when applied to cases of not pure water floods, such as mud/debris floods, produced by landslides. Mud/debris floods are unsteady flow phenomena in which the flow changes rapidly, and the properties of the moving fluid mixture include stop and go mechanisms. The present work reports on a numerical model able to solve the 2D shallow water equations even including bed load transport over erodible bed in realistic situations involving transient flow and movable flow boundaries. The novelty is that it offers accurate and stable results in realistic problems since an appropriate discretization of the governing equations is performed. Furthermore, the present work is focused on the importance of the computational cost. Usually, the main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in realistic cases. However, the proposed model is able to reduce computer times by orders of magnitude making 2D applications competitive and practical for operational flood prediction. Moreover our results show that high performance code development can take advantage of general purpose and inexpensive Graphical Processing Units, allowing to run almost 100 times faster than old generation codes in some cases.",issn="1573-1510",doi="10.1007/s10652-018-09657-7",url="https://doi.org/10.1007/s10652-018-09657-7"} - S. MartÃnez-Aranda, J. Murillo, and P. GarcÃa-Navarro, "A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers," Computers & fluids, 2019.
[Bibtex]@article{MARTINEZARANDA2019,title = "A {1D} numerical model for the simulation of unsteady and highly erosive flows in rivers",journal = "Computers & Fluids",year = "2019",issn = "0045-7930",doi = "https://doi.org/10.1016/j.compfluid.2019.01.011",url = "http://www.sciencedirect.com/science/article/pii/S004579301930009X",author = "S. MartÃnez-Aranda and J. Murillo and P. GarcÃa-Navarro",keywords = "Finite volume method, shallow water equations, Exner equation, coupled method, augmented Roe’s scheme, variable geometry",abstract = "This work is focused on a numerical finite volume scheme for the coupled shallow water-Exner system in 1D applications with arbitrary geometry. The mathematical expressions modeling the hydrodynamic and morphodynamic components of the physical phenomenon are treated to deal with cross-section shape variations and empirical solid discharge estimations. The resulting coupled equations can be rewritten as a non-conservative hyperbolic system with three moving waves and one stationary wave to account for the source terms discretization. Moreover, the wave celerities for the coupled morpho-hydrodyamical system depend on the erosion-deposition mechanism selected to update the channel cross-section profile. This influence is incorporated into the system solution by means of a new parameter related to the channel bottom variation celerity. Special interest is put to show that, even for the simplest solid transport models as the Grass law, to find a linearized Jacobian matrix of the system can be a challenge in presence of arbitrary shape channels. In this paper a numerical finite volume scheme is proposed, based on an augmented Roe solver, first order accurate in time and space, dealing with solid transport flux variations caused by the channel geometry changes. Channel cross-section variations lead to the appearance of a new solid flux source term which should be discretized properly. The stability region is controlled by wave celerities together with a proper reconstruction of the approximate local Riemann problem solution, enforcing positive values for the intermediate states of the conserved variables. Comparison of the numerical results for several analytical and experimental cases demonstrates the effectiveness, exact well-balancedness and accuracy of the scheme."} - A. Navas-Montilla and J. Murillo, "Improved Riemann solvers for an accurate resolution of 1d and 2d shock profiles with application to hydraulic jumps," Journal of computational physics, vol. 378, pp. 445-476, 2019.
[Bibtex]@article{NAVASMONTILLA2019445,title = "Improved {R}iemann solvers for an accurate resolution of 1D and 2D shock profiles with application to hydraulic jumps",journal = "Journal of Computational Physics",volume = "378",pages = "445 - 476",year = "2019",issn = "0021-9991",doi = "https://doi.org/10.1016/j.jcp.2018.11.023",url = "http://www.sciencedirect.com/science/article/pii/S0021999118307496",author = "A. Navas-Montilla and J. Murillo",keywords = "Riemann solver, ARoe, Shallow water, Source terms, Shockwave anomalies, Carbuncle",abstract = "From the early stages of CFD, the computation of shocks using Finite Volume methods has been a very challenging task as they often prompt the generation of numerical anomalies. Such anomalies lead to an incorrect and unstable representation of the discrete shock profile that may eventually ruin the whole solution. The two most widespread anomalies are the slowly-moving shock anomaly and the carbuncle, which are deeply addressed in the literature in the framework of homogeneous problems, such as Euler equations. In this work, the presence of the aforementioned anomalies is studied in the framework of the 1D and 2D SWE and novel solvers that effectively reduce both anomalies, even in cases where source terms dominate the solution, are presented. Such solvers are based on the augmented Roe (ARoe) family of Riemann solvers, which account for the source term as an extra wave in the eigenstructure of the system. The novel method proposed here is based on the ARoe solver in combination with: (a) an improved flux extrapolation method based on a previous work, which circumvents the slowly-moving shock anomaly and (b) a contact wave smearing technique that avoids the carbuncle. The resulting method is able to eliminate the slowly-moving shock anomaly for 1D steady cases with source term. When dealing with 2D cases, the novel method proves to handle complex shock structures composed of hydraulic jumps over irregular bathymetries, avoiding the presence of the aforementioned anomalies."} - I. Echeverribar, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "Use of internal boundary conditions for levees representation: application to river flood management," Environmental fluid mechanics, 2019.
[Bibtex]@Article{GarcÃa-Navarro2019,author="Echeverribar, I.and Morales-Hern{\'a}ndez, M.and Brufau, P.and Garc{\'i}a-Navarro, P.",title="Use of internal boundary conditions for levees representation: application to river flood management",journal="Environmental Fluid Mechanics",year="2019",month="Jan",abstract="River floods can be simulated with the 2D shallow water system of equations using finite volume methods, where the terrain is discretized in cells that form the computational mesh. Usually a proper treatment of wet/dry fronts is required. River levees can be modelled as part of the topography by means of sufficiently small cells of higher elevation than the rest of the bed level in locally refined meshes. This procedure is associated with a large computational time since the time step depends directly on the cell size. The alternative proposed in this work includes the levees as internal boundary conditions in the 2D numerical scheme. In particular, levees have been defined by a weir law that, depending on the relative values of water surface levels on both sides, can formulate the discharge for different situations (i.e. free flow and submerged flow). In addition, having identified numerical difficulties in cases of low discharge under free flow conditions, a novel procedure to avoid oscillations has been developed and called volume transport method. The validation and comparison between methods has been carried out with benchmark test cases and, in addition, with a real flood event in the Ebro River (Spain)",doi="10.1007/s10652-018-09658-6",}
2018
- E. Persi, G. Petaccia, S. Sibilla, P. Brufau, and P. GarcÃa-Navarro, "Calibration of a dynamic Eulerian-lagrangian model for the computation of wood cylinders transport in shallow water flow," Journal of hydroinformatics, vol. 21, iss. 1, pp. 164-179, 2018.
[Bibtex]@article{10.2166/hydro.2018.085,author = {Persi, Elisabetta and Petaccia, Gabriella and Sibilla, Stefano and Brufau, Pilar and GarcÃa-Navarro, Pilar},title = "{Calibration of a dynamic Eulerian-lagrangian model for the computation of wood cylinders transport in shallow water flow}",journal = {Journal of Hydroinformatics},volume = {21},number = {1},pages = {164-179},year = {2018},month = {11},abstract = "{A computational Eulerian–Lagrangian model (ORSA2D\_WT) is used for modelling the movement of floating rigid bodies on the water surface. The two-dimensional transport is computed with a dynamic approach, modifying existing formulations for the transport of bodies within fluid flows for the case of floating bodies, by adopting suitable added mass, drag and side coefficients. An original formulation for planar rotation is proposed, which includes the effect of the hydrodynamic torque and a resistance term, named added inertia, based on the difference between the angular velocity of the flow and that of the body. The value of the added inertia coefficient is calibrated against experiments made on purpose, involving the transport of a cylinder in a flume with two side obstacles. The calibrated code is applied to a slightly larger set of experiments for its preliminary evaluation. The outcome of the simulations shows that the streamwise and transversal displacements are well modelled, while some inaccuracies arise when considering the cylinder orientation. The effects of the initial conditions on the cylinders' trajectory and rotation are discussed, showing their influence on the evolution of the rotation angles.}",issn = {1464-7141},doi = {10.2166/hydro.2018.085},url = {https://doi.org/10.2166/hydro.2018.085},eprint = {https://iwaponline.com/jh/article-pdf/21/1/164/517732/jh0210164.pdf},} - M. Morales-Hernández, J. Murillo, and P. GarcÃa-Navarro, "Diffusion–dispersion numerical discretization for solute transport in 2d transient shallow flows," Environmental fluid mechanics, 2018.
[Bibtex]@Article{Morales-Hernández2018,author="Morales-Hern{\'a}ndez, M.and Murillo, J.and Garc{\'i}a-Navarro, P.",title="Diffusion--dispersion numerical discretization for solute transport in 2D transient shallow flows",journal="Environmental Fluid Mechanics",year="2018",month="Nov",day="01",abstract="The 2D solute transport equation can be incorporated into the 2D shallow water equations in order to solve both flow and solute interactions in a coupled system of equations. In order to solve this system, an explicit finite volume scheme based on Roe's linearization is proposed. Moreover, it is feasible to decouple the solute transport equation from the hydrodynamic system in a conservative way. In this case, the advection part is solved in essence defining a numerical flux, allowing the use of higher order numerical schemes. However, the discretization of the diffusion--dispersion terms have to be carefully analysed. In particular, time-step restrictions linked to the nature of the solute equation itself as well as the numerical diffusion associated to the numerical scheme used are question of interest in this work. These improvements are tested in an analytical case as well as in a laboratory test case with a passive solute (fluorescein) released from a reservoir. Experimental measurements are compared against the numerical results obtained with the proposed model and a sensitivity analysis is carried out, confirming an agreement with the longitudinal coefficients and an underestimation of the transversal ones, respectively.",issn="1573-1510",doi="10.1007/s10652-018-9644-2",url="https://doi.org/10.1007/s10652-018-9644-2"} - M. Morales-Hernández, E. Playán, Y. Gimeno, A. Serreta, and N. Zapata, "Assessing zebra mussel colonization of collective pressurized irrigation networks through pressure measurements and simulations," Agricultural water management, vol. 204, pp. 301-313, 2018.
[Bibtex]@article{MORALESHERNANDEZ2018301,title = "Assessing zebra mussel colonization of collective pressurized irrigation networks through pressure measurements and simulations",journal = "Agricultural Water Management",volume = "204",pages = "301 - 313",year = "2018",issn = "0378-3774",doi = "https://doi.org/10.1016/j.agwat.2018.04.025",url = "http://www.sciencedirect.com/science/article/pii/S0378377418304219",author = "Mario Morales-Hernández and Enrique Playán and Yolanda Gimeno and Alfredo Serreta and Nery Zapata",keywords = ", Hydraulic simulation, Irrigation piping network monitoring, Normalized pressure",abstract = "Zebra mussel (Dreissena polymorpha) colonies are becoming a real problem in pressurized irrigation networks. The zebra mussel infestation of the 45 Water Users Associations (WUAs) of the Riegos del Alto Aragón (RAA) irrigation project (121 thousand hectares located in northeastern Spain) was assessed during the period of 2013â€?017. Maps of WUA infestation stages were produced. A survey of the WUAs made it possible to assess the relevance of certain structural and management practices in the control of zebra mussels. A method to monitor zebra mussel colonization of pressurized collective irrigation networks was presented. The method is based on the combination of pressure measurements at network hydrants and hydraulic simulations. Normalized pressure, estimated as the difference between simulated and observed pressure, should approach zero in all hydrants in a properly characterized, non-infested network. A positive normalized pressure can indicate the presence of zebra mussel colonies. The methodology was validated using two different test cases located in two RAA WUAs: the first case involved a discrete chemical treatment, while the second case was based on the analysis of three years of telemetry pressure data and remote operation of network hydrants. The existence of an infested reservoir upstream of the WUAs was the most likely source of zebra mussel colonization of the WUA pressurized networks in the RAA project. The desiccation and chemical treatment of the small WUA reservoirs was associated with pest control. The hybrid (measurement-simulation) methodology is able to characterize the presence of zebra mussel colonies in specific reaches of pressurized irrigation networks."} - S. MartÃnez-Aranda, J. Fernández-Pato, D. Caviedes-Voullième, I. GarcÃa-PalacÃn, and P. GarcÃa-Navarro, "Towards transient experimental water surfaces: a new benchmark dataset for 2D shallow water solvers," Advances in water resources, vol. 121, pp. 130-149, 2018.
[Bibtex]@Article{camara3D,title = "Towards transient experimental water surfaces: A new benchmark dataset for {2D} shallow water solvers",journal = "Advances in Water Resources",volume = "121",pages = "130 - 149",year = "2018",issn = "0309-1708",doi = "10.1016/j.advwatres.2018.08.013",url = "http://www.sciencedirect.com/science/article/pii/S0309170818303658",author = "S. MartÃnez-Aranda and J. Fernández-Pato and D. Caviedes-Voullième and I. GarcÃa-PalacÃn and P. GarcÃa-Navarro",keywords = "Finite volumes, Shallow water equations, 3D-Sensing, RGB-D Sensor, Transient free-surface flow"ABSTRACT = {In the past decade, shallow water solvers have dramatically improved both in terms of accuracy and computationalpower. New mathematical models and numerical schemes have been systematically verified against 1D exactsolutions and laboratory experiments. Despite the two-dimensional nature of some of these benchmark tests, none ofthem reports complete 2D water depth fields, but only a few profiles are measured and reported in the best case. Thiswork reports a new benchmarking dataset for validation of shallow water solvers, in which two-dimensional transientwater depth measurements are available for complex steady and transient laboratory flume experiments, ranging fromtranscritical steady flow to dam-break flows around obstacles and complex beds. The transient water surface wasmeasured using a commercial-grade RGB-D sensing device which allows to capture a succession of color-coded pointclouds at a high frequency. These experimental measurements are compared with 2D shallow water simulationscarried out with an extensively tested finite volume solver. Results asses the suitability of this dataset to perform asbenchmark tests, identifying potential limitations of current and future models.},} - A. Navas-Montilla and J. Murillo, "2D well-balanced augmented ader schemes for the shallow water equations with bed elevation and extension to the rotating frame," Journal of computational physics, vol. 372, pp. 316-348, 2018.
[Bibtex]@article{NAVASMONTILLA2018316,title = "{2D} well-balanced augmented ADER schemes for the Shallow Water Equations with bed elevation and extension to the rotating frame",journal = "Journal of Computational Physics",volume = "372",pages = "316 - 348",year = "2018",issn = "0021-9991",doi = "https://doi.org/10.1016/j.jcp.2018.06.039",url = "http://www.sciencedirect.com/science/article/pii/S0021999118304170",author = "A. Navas-Montilla and J. Murillo",keywords = "ADER, Shallow water, Source terms, Coriolis, Well-balanced, High order accuracy"} - J. Fernández-Pato and P. GarcÃa-Navarro, "Development of a new simulation tool coupling a 2D finite volume overland flow model and a drainage network model," Geosciences, vol. 8, iss. 8, p. 288, 2018.
[Bibtex]@Article{geosciences8080288,AUTHOR = {Fernández-Pato, Javier and GarcÃa-Navarro, Pilar},TITLE = {Development of a New Simulation Tool Coupling a {2D} Finite Volume Overland Flow Model and a Drainage Network Model},JOURNAL = {Geosciences},VOLUME = {8},YEAR = {2018},NUMBER = {8},PAGES = {288},URL = {http://www.mdpi.com/2076-3263/8/8/288},ISSN = {2076-3263},ABSTRACT = {Numerical simulation of mixed flows combining free surface and pressurized flows is a practical tool to prevent possible flood situations in urban environments. When dealing with intense storm events, the limited capacity of the drainage network conduits can cause undesirable flooding situations. Computational simulation of the involved processes can lead to better management of the drainage network of urban areas. In particular, it is interesting to simultaneuously calculate the possible pressurization of the pipe network and the surface water dynamics in case of overflow. In this work, the coupling of two models is presented. The surface flow model is based on two-dimensional shallow water equations with which it is possible to solve the overland water dynamics as well as the transformation of rainfall into runoff through different submodels of infiltration. The underground drainage system assumes mostly free surface flow that can be pressurized in specific situations. The pipe network is modeled by means of one-dimensional sections coupled with the surface model in specific regions of the domain, such as drains or sewers. The numerical techniques considered for the resolution of both mathematical models are based on finite volume schemes with a first-order upwind discretization. The coupling of the models is verified using laboratory experimental data. Furthermore, the potential usefulness of the approach is demonstrated using real flooding data in a urban environment.},DOI = {10.3390/geosciences8080288}} - D. Caviedes-Voullième, J. Fernández-Pato, and C. Hinz, "Cellular automata and finite volume solvers converge for 2D shallow flow modelling for hydrological modelling," Journal of hydrology, vol. 563, pp. 411-417, 2018.
[Bibtex]@article{CaviedesFernandezPato2018,title = "Cellular Automata and Finite Volume solvers converge for {2D} shallow flow modelling for hydrological modelling",journal = "Journal of Hydrology",volume = "563",pages = "411 - 417",year = "2018",issn = "0022-1694",doi = "10.1016/j.jhydrol.2018.06.021",url = "http://www.sciencedirect.com/science/article/pii/S0022169418304438",author = "Daniel Caviedes-Voullième and Javier Fernández-Pato and Christoph Hinz",keywords = "Surface runoff, Zero-inertia equation, Shallow-water equations, Cellular Automata, Finite Volume, Diffusive-wave equation",abstract = "Surface flows of hydrological interest, including overland flow, runoff, river and channel flow and flooding have received significant attention from modellers in the past 30 years. A growing effort to address these complex environmental problems is in place in the scientific community. Researchers have studied and favoured a plethora of techniques to approach this issue, ranging from very simple empirically-based mathematical models, to physically-based, deductive and very formal numerical integration of systems of partial-differential equations. In this work, we review two families of methods: cell-based simulators â€?later called Cellular Automata â€?and Finite Volume solvers for the Zero-Inertia equation, which we show to converge into a single methodology given appropriate choices. Furthermore, this convergence, mathematically shown in this work, can also be identified by critically reviewing the existing literature, which leads to the conclusion that two methods originating from different reasoning and fundamental philosophy, fundamentally converge into the same method. Moreover, acknowledging such convergence allows for some generalisation of properties of numerical schemes such as error behaviour and stability, which, importantly, is the same for the converging methodology, a fact with practical implications. Both the review of existing literature and reasoning in this work attempts to aid in the effort of synchronising and cross-fertilizing efforts to improve the understanding and the outlook of Zero-Inertia solvers for surface flows, as well as to help in clarifying the possible confusion and parallel developments that may arise from the use of different terminology originating from historical reasons. Moreover, synchronising and unifying this knowledge-base can help clarify model capabilities, applicability and modelling issues for hydrological modellers, specially for those not deeply familiar with the mathematical and numerical details."} - J. Fernández-Pato, J. L. Gracia, and P. GarcÃa-Navarro, "A fractional-order infiltration model to improve the simulation of rainfall/runoff in combination with a 2D Shallow Water model," Journal of hydroinformatics, vol. 20, iss. 4, pp. 898-916, 2018.
[Bibtex]@article{FernandezPato2018a,title = "A fractional-order infiltration model to improve the simulation of rainfall/runoff in combination with a 2{D} {S}hallow {W}ater model",journal = "Journal of Hydroinformatics",volume = "20",number = "4",pages = "898-916",year = "2018",note = "",doi = "10.2166/hydro.2018.145",author = "J. Fern{\'a}ndez-Pato and J.L. Gracia and P. Garc{\'i}a-Navarro",abstract = "In this work, a distributed 2D Shallow Water (SW) flow model is combined with a fractional-order version of the Green-Ampt (FOGA) infiltration law to improve rainfall/runoff simulation in real catchments. The surface water model is based on a robust finite volume method on triangular grids that can handle flow over dry bed and multiple wet/dry fronts. When supplied with adequate infiltration laws, this model can provide useful information in surface Hydrology. The classical Green-Ampt law is generalized by using a Caputo fractional derivative of order less than or equal to 1 in Darcy's law. The novelty of this combination is that, on the one hand, the distributed SW simulation provides a detailed surface water distribution and, on the other hand, the FOGA model offers the possibility to model infiltration rates not monotonically decreasing. In order to obtain the best results, a non-uniform order of the fractional derivative depending on the cumulative infiltration and the existence of available surface water is proposed for realistic cases. This allows to improve significantly previous published numerical results in the literature for several storm events on catchments where the infiltration process occurs."} - A. Lacasta, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations," Journal of hydraulic research, vol. 56, iss. 1, pp. 111-123, 2018.
[Bibtex]@article{doi:10.1080/00221686.2017.1300196,author = {Asier Lacasta and Mario Morales-Hernández and Pilar Brufau and Pilar GarcÃa-Navarro},title = {Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations},journal = {Journal of Hydraulic Research},volume = {56},number = {1},pages = {111-123},year = {2018},publisher = {Taylor & Francis},doi = {10.1080/00221686.2017.1300196},URL = {https://doi.org/10.1080/00221686.2017.1300196},eprint = {https://doi.org/10.1080/00221686.2017.1300196}} - C. Juez, A. Tena, J. Fernández-Pato, R. J. Batalla, and P. GarcÃa-Navarro, "Application of a distributed 2D overland flow model for a rainfall/runoff and erosion simulation in a mediterranean watershed," Cuadernos de investigación geográfica, vol. 44, iss. 2, pp. 615-640, 2018.
[Bibtex]@article{Juez2018,title = "Application of a distributed {2D} overland flow model for a rainfall/runoff and erosion simulation in a Mediterranean watershed",journal = "Cuadernos de Investigación Geográfica",volume = "44",number = "2",pages = "615 - 640",year = "2018",note = "",doi = "https://publicaciones.unirioja.es/ojs/index.php/cig/issue/view/196",author = "C. Juez and A. Tena and J. Fern{\'a}ndez-Pato and R.J. Batalla and P. Garc{\'i}a-Navarro",abstract = "Soil erosion has reemerged as an environmental problem associated with climate change thatrequires the help of simulation tools for forecasting future consequences. This topic becomes even morerelevant in Mediterranean catchments due to the highly variable and irregular rainfall regime. Hence, anapproach that includes the rainfall/runoff and erosion phenomena is required for quantifying the amountof soil the catchments are transferring to the rivers. As the calibration process of the infiltration and erosionparameters can become cumbersome in terms of iterations to the optimal values to fit experimental data, aSimplified Catchment Model (SCM) is introduced as a first approach. The set of tuning constants thatprovides the best fit are used as input for re-calibrating the parameters by means of the simulation of thereal catchment. The modeling effort here presented opens its application to the analysis of the hydro-sedimentary processes at larger temporal and spatial scales."} - J. Fernández-Pato, M. Morales-Hernández, and P. GarcÃa-Navarro, "Implicit finite volume simulation of 2D shallow water flows in flexible meshes," Computer methods in applied mechanics and engineering, vol. 328, pp. 1-25, 2018.
[Bibtex]@article{FernandezPato2017a,title = "Implicit finite volume simulation of {2D} shallow water flows in flexible meshes",journal = "Computer Methods in Applied Mechanics and Engineering",volume = "328",number = "",pages = "1 - 25",year = "2018",note = "",doi = "10.1016/j.cma.2017.08.050",url = "http://www.sciencedirect.com/science/article/pii/S0045782517302724",author = "J. Fern{\'a}ndez-Pato and M. Morales-Hern{\'a}ndez and P. Garc{\'i}a-Navarro",abstract = "In this work, an implicit method for solving 2D hyperbolic systems of equations is presented, focusing on the application to the 2D shallow water equations. It is based on the first order Roe’s scheme, in the framework of finite volume methods. A conservative linearization is done for the flux terms, leading to a non-structured matrix for unstructured meshes thus requiring iterative methods for solving the system. The validation is done by comparing numerical and exact solutions in both unsteady and steady cases. In order to test the applicability of the implicit scheme to real world situations, a laboratory scale tsunami simulation is carried out and compared to the experimental data. The implicit schemes have the advantage of the unconditional stability, but a quality loss in the transient solution can appear for high CFL numbers. The properties of the scheme are well suited for the simulation of unsteady shallow water flows over irregular topography using all kind of meshes."}
2017
- D. Caviedes-Voullième, M. Morales-Hernández, C. Juez, A. Lacasta, and P. GarcÃa-Navarro, "Two-dimensional numerical simulation of bed-load transport of a finite-depth sediment layer: applications to channel flushing," Journal of hydraulic engineering, vol. 143, iss. 9, p. 4017034, 2017.
[Bibtex]@article{doi:10.1061/(ASCE)HY.1943-7900.0001337,author = {Daniel Caviedes-Voullième and Mario Morales-Hernández and Carmelo Juez and Asier Lacasta and Pilar GarcÃa-Navarro },title = {Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing},journal = {Journal of Hydraulic Engineering},volume = {143},number = {9},pages = {04017034},year = {2017},doi = {10.1061/(ASCE)HY.1943-7900.0001337}URL = {https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29HY.1943-7900.0001337},eprint = {https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29HY.1943-7900.0001337},abstract = { Numerical modeling of bed-load transport in shallow flows, particularly oriented toward environmental flows, is an active field of research. Nevertheless, other possible applications exist. In particular, bed-load transport phenomena are relevant in urban drainage systems, including sewers. However, few applications of coupled two-dimensional (2D) shallow-water and bed-load transport models can be found, and their transfer from environmental applications—usually river and floodplain—into sewer applications requires some adaptation. Unlike to river systems, where there is a thick layer of sediment that constitutes a movable riverbed, sewer systems have thin layers of sediment that need to be removed, thus exposing a rigid, nonerodible surface. This problem requires careful numerical treatment to avoid generating errors and instability in the simulation. This paper deals with a numerical approach to tackle this issue in an efficient way that allows large-scale studies to be performed and provides empirical evidence that the proposed approach is accurate and applicable for sewage and channel-flushing problems. }} - C. Juez, S. Soares-Frazao, J. Murillo, and P. GarcÃa-Navarro, "Experimental and numerical simulation of bed load transport over steep slopes," Journal of hydraulic research, vol. 55, iss. 4, pp. 455-469, 2017.
[Bibtex]@article{Juez2017,author = {Carmelo Juez and Sandra Soares-Frazao and Javier Murillo and Pilar GarcÃa-Navarro},title = {Experimental and numerical simulation of bed load transport over steep slopes},journal = {Journal of Hydraulic Research},volume = {55},number = {4},pages = {455-469},year = {2017},publisher = {Taylor & Francis},doi = {10.1080/00221686.2017.1288417},URL = {https://doi.org/10.1080/00221686.2017.1288417},eprint = {https://doi.org/10.1080/00221686.2017.1288417}} - A. Navas-Montilla and J. Murillo, "Overcoming numerical shockwave anomalies using energy balanced numerical schemes. application to the shallow water equations with discontinuous topography," Journal of computational physics, vol. 340, pp. 575-616, 2017.
[Bibtex]@article{NavasMontilla2017575,title = "Overcoming numerical shockwave anomalies using energy balanced numerical schemes. Application to the Shallow Water Equations with discontinuous topography ",journal = "Journal of Computational Physics ",volume = "340",number = "",pages = "575 - 616",year = "2017",note = "",issn = "0021-9991",doi = "https://doi.org/10.1016/j.jcp.2017.03.057",url = "http://www.sciencedirect.com/science/article/pii/S0021999117302589",author = "A. Navas-Montilla and J. Murillo",keywords = "Roe solver",keywords = "Energy balanced",keywords = "Shallow water",keywords = "Source terms",keywords = "Hydraulic jump",keywords = "Postshock oscillations ",abstract = "When designing a numerical scheme for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced \{STD\} based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the \{STD\} procedure required should not be merely based on ad hoc approximations. The \{STD\} proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the \{STD\} must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some numerical anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative \{STD\} that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the \{SWE\} containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though it does not disturb the rest of the solution in steady cases, when considering transient cases it produces a very undesirable shedding of spurious oscillations downstream that should be circumvented. Based on spike-reducing techniques (originally designed for homogeneous Euler equations) that propose the construction of interpolated fluxes in the untrustworthy regions, we design a novel Roe-type scheme for the \{SWE\} with discontinuous topography that reduces the presence of the aforementioned spurious spike. The resulting spike-reducing method in combination with the proposed \{STD\} ensures an accurate positioning of steady jumps, provides convergence with mesh refinement, which was not possible for previous methods that cannot avoid the spike. "} - A. Lacasta, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations," Journal of hydraulic research, pp. 1-13, 2017.
[Bibtex]@article{Lacasta2017BoundaryAdjoint,author = {Asier Lacasta and Mario Morales-Hern{\'a}ndez and Pilar Brufau and Pilar Garc\'ia-Navarro},title = {Application of an adjoint-based optimization procedure for the optimal control of internal boundary conditions in the shallow water equations},journal = {Journal of Hydraulic Research},volume = {0},number = {0},pages = {1-13},year = {2017},doi = {10.1080/00221686.2017.1300196},URL = {http://dx.doi.org/10.1080/00221686.2017.1300196},eprint = {http://dx.doi.org/10.1080/00221686.2017.1300196},abstract = { The shallow water equations have been extensively studied and used to model unsteady open channel flows in different applications. They belong to the category of hyperbolic partial differential equations and their treatment has recently been benefited from many numerical contributions leading to robust, accurate and well-balanced solutions. The correct formulation of external and internal boundary conditions is required to achieve a useful model in practical application. Control of internal boundary conditions may be useful in water distribution facilities. Therefore, development of a control strategy based on the fully dynamical mathematical model becomes attractive and justified. This work is devoted to the implementation of an adjoint based sensitivity analysis for the control of sluice gates in open-channel flow, formulated as internal boundary conditions. This is one of the most complex tasks in multiple regulated water delivery situations. Based on gradient method optimizers, the control of the whole channel to satisfy different requirements at several points of the channel is discussed. One of the achievements in this work is that the whole optimization process is performed two orders of magnitude faster than in real time. Moreover, the numerical results show this promising technique is a feasible way to obtain a robust and efficient control method. }} - M. Morales-Hernández, A. Lacasta, J. Murillo, and P. GarcÃa-Navarro, "A Large Time Step explicit scheme (CFL>1) on unstructured grids for 2D conservation laws: application to the homogeneous shallow water equations," Applied mathematical modelling, vol. 47, pp. 294-317, 2017.
[Bibtex]@article{MoralesHernandez2017294,title = "A {L}arge {T}ime {S}tep explicit scheme ({CFL}>1) on unstructured grids for 2{D} conservation laws: Application to the homogeneous shallow water equations ",journal = "Applied Mathematical Modelling ",volume = "47",number = "",pages = "294 - 317",year = "2017",note = "",issn = "0307-904X",doi = "http://dx.doi.org/10.1016/j.apm.2017.02.043",url = "http://www.sciencedirect.com/science/article/pii/S0307904X17301397",author = "M. Morales-Hern{\'a}ndez and A. Lacasta and J. Murillo and P. Garc\'ia-Navarro",keywords = "Unstructured grids",keywords = "Large Time Step",keywords = "CFL > 1",keywords = "2D conservation laws",keywords = "Shallow water equations ",abstract = "In this work, a {L}arge {T}ime {S}tep (LTS) explicit finite volume scheme designed to allow \{CFL\} > 1 is applied to the numerical resolution of 2D scalar and systems of conservation laws on triangular grids. Based on the flux difference splitting formulation, a special concern is put on finding the way of packing the information to compute the numerical solution when working on unstructured grids. Not only the cell areas but also the length of the interfaces and their orientation are questions of interest to send the information from each edge or interface. The information to update the cell variables is computed according to the local average discrete velocity and the orientation of the edges of the cells involved. The performance of these ideas is tested and compared with the conventional explicit first order and second order schemes in academic configurations for the 2D linear scalar equation and for 2D systems of conservation laws (in particular the shallow water equations) without source terms. The \{LTS\} scheme is demonstrated to preserve or even gain accuracy and save computational time with respect to the first order scheme. "} - I. Echeverribar, M. Morales-Hernández, A. Lacasta, P. Brufau, and P. GarcÃa-Navarro, "Simulación numérica con RiverFlow2D de posibles soluciones de mitigación de avenidas en el tramo medio del rÃo Ebro," IngenierÃa del agua, vol. 21, iss. 1, pp. 53-70, 2017.
[Bibtex]@article{Echeverribar2016,title = "Simulación numérica con {R}iver{F}low2{D} de posibles soluciones de mitigación de avenidas en el tramo medio del rÃo {E}bro",journal = "Ingenier\'{i}a del agua ",volume = "21",number = "1",pages = "53-70",year = "2017",doi = {10.4995/ia.2017.6550},URL = {http://polipapers.upv.es/index.php/IA/article/download/6550/pdf},eprint = {http://dx.doi.org/10.4995/ia.2017.6550},author = "Isabel Echeverribar and Mario Morales-Hern{\'a}ndez and Asier Lacasta and Pilar Brufau and Pilar Garc\'ia-Navarro",abstract = "En este trabajo se presenta un estudio de medidas orientadas a la mitigación de avenidas en el tramo medio del rÃo Ebro: limpieza de vegetación del cauce, uso de zonas de inundación controlada y construcción o re-adaptación de motas. Para ello se utiliza el software RiverFlow2D que resuelve las ecuaciones conservativas del flujo de superficie libre con un método de volúmenes finitos realizando los cálculos sobre GPU. Se comparan los resultados con medidas en estaciones de aforo e información extraÃda de ortofotos. La medida más efectiva, de las analizadas, ha resultado ser la eliminación de la vegetación en el cauce. Se demuestra que no sólo el área máxima inundada es menor en todo el tramo sino que también reduce la altura de agua hasta en 1 m. El resto de medidas tienen consecuencias locales y de poca entidad cuando los caudales pico son altos, aunque podrÃan resultar de utilidad para avenidas con caudales más bajos."} - A. Lacasta, M. Morales-Hernández, J. Burguete, P. Brufau, and P. GarcÃa-Navarro, "Calibration of the 1D shallow water equations: a comparison of Monte Carlo and gradient-based optimization methods," Journal of hydroinformatics, 2017.
[Bibtex]@article {Lacastajh2017021,author = {Lacasta, Asier and Morales-Hern{\'a}ndez, Mario and Burguete, Javier and Brufau, Pilar and Garc\'ia-Navarro, Pilar},title = {Calibration of the 1{D} shallow water equations: a comparison of {M}onte {C}arlo and gradient-based optimization methods},year = {2017},doi = {10.2166/hydro.2017.021},publisher = {IWA Publishing},abstract = {The calibration of parameters in complex systems usually requires a large computational effort. Moreover, it becomes harder to perform the calibration when non-linear systems underlie the physical process, and the direction to follow in order to optimize an objective function changes depending on the situation. In the context of shallow water equations (SWE), the calibration of parameters, such as the roughness coefficient or the gauge curve for the outlet boundary condition, is often required. In this work, the SWE are used to simulate an open channel flow with lateral gates. Due to the uncertainty in the mathematical modeling that these lateral discharges may introduce into the simulation, the work is focused on the calibration of discharge coefficients. Thus, the calibration is performed by two different approaches. On the one hand, a classical Monte Carlo method is used. On the other hand, the development and application of an adjoint formulation to evaluate the gradient is presented. This is then used in a gradient-based optimizer and is compared with the stochastic approach. The advantages and disadvantages are illustrated and discussed through different test cases.},issn = {1464-7141},URL = {http://jh.iwaponline.com/content/early/2017/01/06/hydro.2017.021},eprint = {http://jh.iwaponline.com/content/early/2017/01/06/hydro.2017.021.full.pdf},journal = {Journal of Hydroinformatics}}
2016
- C. Juez, J. Murillo, and P. GarcÃa-Navarro, "One-dimensional riemann solver involving variable horizontal density to compute unsteady sediment transport," Journal of hydraulic engineering, vol. 142, iss. 3, p. 4015056, 2016.
[Bibtex]@article{doi:10.1061/(ASCE)HY.1943-7900.0001082,author = {C. Juez and J. Murillo and P. GarcÃa-Navarro },title = {One-Dimensional Riemann Solver Involving Variable Horizontal Density to Compute Unsteady Sediment Transport},journal = {Journal of Hydraulic Engineering},volume = {142},number = {3},pages = {04015056},year = {2016},doi = {10.1061/(ASCE)HY.1943-7900.0001082}URL = {https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29HY.1943-7900.0001082},eprint = {https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29HY.1943-7900.0001082},abstract = { Intense transient shallow flows over erodible bed imply the appearance of a changing horizontal density attributable to the presence of sediment particles in the water layer. The lack of consideration of the variability of the bulking density of the mixture is not admissible when modeling severe types of erosional flow such as the release of a dam break wave over a sedimentary bottom. Such events can lead to significant changes in the wave hydrodynamics, since the inertia of the flow can be larger and consequently its erosion/deposition capacity can be altered. From a numerical point of view a new complex erosion/deposition source term appears. For the integration of these source terms two strategies have been explored in this work: upwind and pointwise. Hence, this work is focused on the development and validation of a novel numerical scheme based on an approximate augmented Riemann solver, where the erosion/deposition rates play an important role in the variation of mixture density. Several analytical test cases have been derived in order to validate the computational tool. The numerical predictions have also been compared against experimental data. }} - J. Murillo and A. Navas-Montilla, "A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. application to the 1D-2D shallow water equations," Advances in water resources, vol. 98, pp. 70-96, 2016.
[Bibtex]@article{Murillo201670,title = "A comprehensive explanation and exercise of the source terms in hyperbolic systems using {R}oe type solutions. Application to the 1{D}-2{D} shallow water equations ",journal = "Advances in Water Resources ",volume = "98",number = "",pages = "70 - 96",year = "2016",note = "",issn = "0309-1708",doi = "http://dx.doi.org/10.1016/j.advwatres.2016.10.019",url = "http://www.sciencedirect.com/science/article/pii/S0309170816305917",author = "J. Murillo and A. Navas-Montilla",keywords = "Hyperbolic systems",keywords = "Stopping conditions",keywords = "Source terms",keywords = "Well-balanced",keywords = "Energy-balanced",keywords = "Wet/dry front ",abstract = "Abstract Powerful numerical methods have to consider the presence of source terms of different nature, that intensely compete among them and may lead to strong spatiotemporal variations in the flow. When applied to shallow flows, numerical preservation of quiescent equilibrium, also known as the well-balanced property, is still nowadays the keystone for the formulation of novel numerical schemes. But this condition turns completely insufficient when applied to problems of practical interest. Energy balanced methods (E-schemes) can overcome all type of situations in shallow flows, not only under arbitrary geometries, but also with independence of the rheological shear stress model selected. They must be able to handle correctly transient problems including modeling of starting and stopping flow conditions in debris flow and other flows with a non-Newtonian rheological behavior. The numerical solver presented here satisfies these properties and is based on an approximate solution defined in a previous work. Given the relevant capabilities of this weak solution, it is fully theoretically derived here for a general set of equations. This useful step allows providing for the first time an E-scheme, where the set of source terms is fully exercised under any flow condition involving high slopes and arbitrary shear stress. With the proposed solver, a Roe type first order scheme in time and space, positivity conditions are explored under a general framework and numerical simulations can be accurately performed recovering an appropriate selection of the time step, allowed by a detailed analysis of the approximate solver. The use of case-dependent threshold values is unnecessary and exact mass conservation is preserved. "} - A. Navas-Montilla and J. Murillo, "Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms," Journal of computational physics, vol. 317, pp. 108-147, 2016.
[Bibtex]@article{NavasMontilla2016108,title = "Asymptotically and exactly energy balanced augmented flux-{ADER} schemes with application to hyperbolic conservation laws with geometric source terms ",journal = "Journal of Computational Physics ",volume = "317",number = "",pages = "108 - 147",year = "2016",note = "",issn = "0021-9991",doi = "http://dx.doi.org/10.1016/j.jcp.2016.04.047",url = "http://www.sciencedirect.com/science/article/pii/S0021999116301024",author = "A. Navas-Montilla and J. Murillo",keywords = "ADER",keywords = "HLL solver",keywords = "Energy balanced",keywords = "Shallow water",keywords = "Source terms",keywords = "High order accuracy ",abstract = "Abstract In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) [1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the \{FS\} solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the \{FS\} solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed \{FS\} and \{LFS\} solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed. "} - A. Lacasta and P. GarcÃa-Navarro, "A GPU accelerated adjoint-based optimizer for inverse modeling of the two-dimensional shallow water equations," Computers & fluids, vol. 136, pp. 371-383, 2016.
[Bibtex]@article{Lacasta2016371,title = "A {GPU} accelerated adjoint-based optimizer for inverse modeling of the two-dimensional shallow water equations ",journal = "Computers & Fluids ",volume = "136",number = "",pages = "371 - 383",year = "2016",note = "",issn = "0045-7930",doi = {10.1016/j.compfluid.2016.06.024},url = "http://www.sciencedirect.com/science/article/pii/S0045793016302092",author = "A. Lacasta and P. GarcÃa-Navarro",keywords = "Adjoint method",keywords = "Shallow water equations",keywords = "Free-surface flow",keywords = "Quasi-Newton methods",keywords = "Checkpointing",keywords = "GPU computing "} - C. Juez, A. Lacasta, J. Murillo, and P. GarcÃa-Navarro, "An efficient GPU implementation for a faster simulation of unsteady bed-load transport," Journal of hydraulic research, vol. 54, iss. 3, pp. 275-288, 2016.
[Bibtex]@article{doi:10.1080/00221686.2016.1143042,author = {Carmelo Juez and Asier Lacasta and Javier Murillo and Pilar GarcÃa-Navarro},title = {An efficient {GPU} implementation for a faster simulation of unsteady bed-load transport},journal = {Journal of Hydraulic Research},volume = {54},number = {3},pages = {275-288},year = {2016},doi = {10.1080/00221686.2016.1143042},URL = {http://dx.doi.org/10.1080/00221686.2016.1143042},eprint = {http://dx.doi.org/10.1080/00221686.2016.1143042},abstract = { ABSTRACTComputational tools may help engineers in the assessment of sediment transport during the decision-making processes. The main requirements are that the numerical results have to be accurate and simulation models must be fast. The present work is based on the 2D shallow water equations in combination with the 2D Exner equation. The resulting numerical model accuracy was already discussed in previous work. Regarding the speed of the computation, the Exner equation slows down the already costly 2D shallow water model as the number of variables to solve is increased and the numerical stability is more restrictive. In order to reduce the computational effort required for simulating realistic scenarios, the authors have exploited the use of Graphics Processing Units in combination with non-trivial optimization procedures. The gain in computing cost obtained with the graphic hardware is compared against single-core (sequential) and multi-core (parallel) CPU implementations in two unsteady cases. }} - J. Fernández-Pato and P. GarcÃa-Navarro, "2D zero-inertia model for solution of overland flow problems in flexible meshes," Journal of hydrologic engineering, p. 4016038, 2016.
[Bibtex]@article{FernándezPato2016b,author = {J. Fernández-Pato and P. GarcÃa-Navarro},title = {{2D} Zero-Inertia Model for Solution of Overland Flow Problems in Flexible Meshes},journal = {Journal of Hydrologic Engineering},volume = {0},number = {0},pages = {04016038},year = {2016},doi = {10.1061/(ASCE)HE.1943-5584.0001428},URL = {http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001428},eprint = {http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001428},abstract = {A study of the efficiency of a Zero-Inertia model for 2D overland flow simulation is presented in this work. An upwind numerical scheme is used for the spatial discretization in the frame of finite volume methods and an implicit formulation is chosen to avoid numerical instability. The scheme is applied in both structured and unstructured meshes, focusing in the last ones, due to their good adaptability. The Zero-Inertia equation has a non-linear character, hence a linearization is required in the implicit procedure. This is carried out by means of Picard iterations method as a previous step to the system matrix resolution, characteristic of implicit techniques. The BiConjugate Gradient Stabilized (BiCGStab) method combined with sparse storage strategies is selected for the system resolution. A dual threshold Incomplete LU factorization (ILUT) is chosen as matrix preconditioner. Computational efficiency of the implicit temporal discretization for Zero-Inertia model is explored under both steady and unsteady flow conditions by comparing the CPU times against the explicit version of the same model.}} - J. Fernández-Pato and P. GarcÃa-Navarro, "Simulación numérica de inundación de valles fluviales mediante un modelo difusivo implÃcito," IngenierÃa del agua, vol. 20, iss. 3, pp. 115-126, 2016.
[Bibtex]@article{FernándezPato2016c,title = "Simulación numérica de inundación de valles fluviales mediante un modelo difusivo implÃcito",journal = "Ingenier\'{i}a del agua ",volume = "20",number = "3",pages = "115-126",year = "2016",doi = {10.4995/ia.2016.4548},URL = {http://dx.doi.org/10.4995/ia.2016.4548},eprint = {http://dx.doi.org/10.4995/ia.2016.4548},author = "Javier Fernández-Pato and Pilar GarcÃa-Navarro",abstract = "En este trabajo se presenta un modelo difusivo de flujo superficial para la resolución eficiente de problemas de inundación de valles fluviales. La discretización espacial se realiza mediante un esquema upwind de volúmenes finitos, aplicado en una malla triangular no estructurada. Para la discretización temporal se ha empleado un esquema implÃcito, lo que conlleva la generación de un sistema de tantas ecuaciones como celdas de cálculo tenga la malla computacional. Para su resolución, se ha empleado el método del Gradiente Biconjugado Estabilizado (BiCGStab). La eficiencia computacional se mide realizando una comparación de tiempos de CPU de las versiones explÃcita e implÃcita del mismo esquema numérico aplicado al modelo de onda difusiva. El estudio demuestra que, en general, el modelo difusivo se beneficia de una discretización temporal implÃcita, aumentando su eficiencia en gran medida frente al uso de un esquema explÃcito. Debido al carácter no lineal de la ecuación difusiva, un paso de tiempo mayor no siempre garantiza un menor coste computacional y resulta necesario encontrar el paso de tiempo óptimo para cada problema. Se ha aplicado el modelo difusivo a un caso test de inundación de valle fluvial propuesto por la UK Environmetal Agency para evaluar su capacidad predictiva en relación a modelos comerciales. Por último, se han comparado los resultados de calado y nivel de agua proporcionados por el modelo propuesto con los generados por una formulación matemática basada en las ecuaciones completas de aguas poco profundas no encontrándose diferencias relevantes en el ejemplo analizado."} - F. Segura-Beltrán, C. Sanchis-Ibor, M. Morales-Hernández, M. González-Sanchis, G. Bussi, and E. Ortiz, "Using post-flood surveys and geomorphologic mapping to evaluate hydrological and hydraulic models: The flash flood of the Girona River (Spain) in 2007," Journal of hydrology, p. -, 2016.
[Bibtex]@article{SeguraBeltran2016,title = "Using post-flood surveys and geomorphologic mapping to evaluate hydrological and hydraulic models: {T}he flash flood of the {G}irona {R}iver ({S}pain) in 2007 ",journal = "Journal of Hydrology ",volume = "",number = "",pages = " - ",year = "2016",note = "",issn = "0022-1694",doi = "10.1016/j.jhydrol.2016.04.039",url = "http://www.sciencedirect.com/science/article/pii/S002216941630230X",author = "F. Segura-Beltrán and C. Sanchis-Ibor and M. Morales-Hernández and M. González-Sanchis and G. Bussi and E. Ortiz",keywords = "Flash floods",keywords = "Hydrological modeling",keywords = "Hydraulic modeling",keywords = "Alluvial fans",keywords = "Post-flood surveys",keywords = "Geomorphologic mapping ",abstract = "Summary This paper analyzes the Girona River (Spain) flash flood, occurred on the 12th of October 2007, combining hydrological and hydraulic modeling with geomorphologic mapping and post-flood survey information. This research aims to reproduce the flood event in order to understand and decipher the flood processes and dynamics on a system of prograding alluvial fans. The hydrological model \{TETIS\} was used to characterize the shape and dimension of the October 2007 Girona River hydrograph. Subsequently, the flood event was reproduced using the free surface flow module of the model RiverFlow2D. The combination of hydrological and hydraulic models was evaluated using post-flood surveys defining maximum flooded area and flood depths. Then, simulations with different peak discharges were carried out to estimate the hydro-geomorphologic response of the Girona River floodplain, through the identification of the activation thresholds in different geomorphic elements. Results showed that the unit peak discharge of the October 2007 flood event (5 m3 sâˆ? kmâˆ?) was among the largest ever recorded in the area, according to the existing literature. Likewise, the hydraulic model showed a good performance in reproducing the flood event (FitA = 76\%, \{RMSE\} = 0.65 m and \{NSE\} = 0.6), despite the complexity of the case, an ephemeral and ungauged river. The model simulation revealed the existence of an activation pattern of paleochannels and alluvial fans, which was altered by the presence of some anthropogenic disturbances. This multidisciplinary approach proved to be a useful strategy for understanding flash flood processes in ungauged catchments. It allowed understanding the mechanisms governing floods in alluvial fans systems and it represented a solid contribution for early warning plans and risk mitigation policies. "} - J. Fernández-Pato, D. Caviedes-Voullième, and P. GarcÃa-Navarro, "Rainfall/runoff simulation with 2D full shallow water equations: sensitivity analysis and calibration of infiltration parameters," Journal of hydrology, vol. 536, pp. 496-513, 2016.
[Bibtex]@article{FernándezPato2016496,title = "Rainfall/runoff simulation with {2D} full shallow water equations: Sensitivity analysis and calibration of infiltration parameters ",journal = "Journal of Hydrology ",volume = "536",number = "",pages = "496 - 513",year = "2016",note = "",issn = "0022-1694",doi = "doi:10.1016/j.jhydrol.2016.03.021",url = "http://www.sciencedirect.com/science/article/pii/S0022169416301263",author = "Javier Fernández-Pato and Daniel Caviedes-Voullième and Pilar GarcÃa-Navarro",keywords = "Finite volumes",keywords = "Shallow-water equations",keywords = "Hydrologic modeling",keywords = "Infiltration models",keywords = "Rain-runoff generation ",abstract = "Summary One of the most difficult issues in the development of hydrologic models is to find a rigorous source of data and specific parameters to a given problem, on a given location that enable reliable calibration. In this paper, a distributed and physically based model (2D Shallow Water Equations) is used for surface flow and runoff calculations in combination with two infiltration laws (Horton and Green–Ampt) for estimating infiltration in a watershed. This technique offers the capability of assigning a local and time-dependent infiltration rate to each computational cell depending on the available surface water, soil type or vegetation. We investigate how the calibration of parameters is affected by transient distributed Shallow Water model and the complexity of the problem. In the first part of this work, we calibrate the infiltration parameters for both Horton and Green–Ampt models under flat ponded soil conditions. Then, by means of synthetic test cases, we perform a space-distributed sensitivity analysis in order to show that this calibration can be significantly affected by the introduction of topography or rainfall. In the second part, parameter calibration for a real catchment is addressed by comparing the numerical simulations with two different sets of experimental data, corresponding to very different events in terms of the rainfall volume. We show that the initial conditions of the catchment and the rainfall pattern have a special relevance in the quality of the adjustment. Hence, it is shown that the topography of the catchment and the storm characteristics affect the calibration of infiltration parameters. "} - A. Navas-Montilla and J. Murillo, "Asymptotically and exactly energy balanced augmented flux-ader schemes with application to hyperbolic conservation laws with geometric source terms," Journal of computational physics, vol. 317, pp. 108-147, 2016.
[Bibtex]@article{NavasMontilla2016108,title = "Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms ",journal = "Journal of Computational Physics ",volume = "317",number = "",pages = "108 - 147",year = "2016",note = "",issn = "0021-9991",doi = "http://dx.doi.org/10.1016/j.jcp.2016.04.047",url = "http://www.sciencedirect.com/science/article/pii/S0021999116301024",author = "A. Navas-Montilla and J. Murillo",keywords = "ADER",keywords = "HLL solver",keywords = "Energy balanced",keywords = "Shallow water",keywords = "Source terms",keywords = "High order accuracy ",abstract = "Abstract In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) [1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the \{FS\} solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the \{FS\} solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed \{FS\} and \{LFS\} solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed. "} - C. Juez, C. Ferrer-Boix, J. Murillo, M. A. Hassan, and P. GarcÃa-Navarro, "A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds," Advances in water resources, vol. 87, pp. 1-18, 2016.
[Bibtex]@article{Juez20161,title = "A model based on {H}irano-{E}xner equations for two-dimensional transient flows over heterogeneous erodible beds ",journal = "Advances in Water Resources ",volume = "87",number = "",pages = "1 - 18",year = "2016",note = "",issn = "0309-1708",doi = "10.1016/j.advwatres.2015.10.013",url = "http://www.sciencedirect.com/science/article/pii/S0309170815002584",author = "C. Juez and C. Ferrer-Boix and J. Murillo and M.A. Hassan and P. GarcÃa-Navarro",keywords = "2D shallow water equations",keywords = "Exner equation",keywords = "Hirano equation",keywords = "Sorting celerities",keywords = "Heterogeneous material",keywords = "Dynamically chosen time-step ",abstract = "Abstract In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data. "} - M. Morales-Hernández, G. Petaccia, P. Brufau, and P. GarcÃa-Navarro, "Conservative 1D–2D coupled numerical strategies applied to river flooding: The Tiber (Rome)," Applied mathematical modelling, vol. 40, iss. 3, pp. 2087-2105, 2016.
[Bibtex]@article{MoralesHernández20162087,title = "Conservative {1D}–{2D} coupled numerical strategies applied to river flooding: {T}he {T}iber ({R}ome) ",journal = "Applied Mathematical Modelling ",volume = "40",number = "3",pages = "2087 - 2105",year = "2016",note = "",issn = "0307-904X",doi = "10.1016/j.apm.2015.08.016",url = "http://www.sciencedirect.com/science/article/pii/S0307904X15005375",author = "M. Morales-Hernández and G. Petaccia and P. Brufau and P. GarcÃa-Navarro",keywords = "1Dâ€?D coupled model",keywords = "Shallow water",keywords = "Conservation",keywords = "River flooding ",abstract = "Abstract Coupled 1Dâ€?D numerical strategies are presented in this work for their application to fast computation of large rivers flooding. Both 1D and 2D models are built using explicit upwind finite volume schemes, able to deal with wetting-drying fronts. The topography representation is described via cross sections for the 1D model and with quadrilateral/triangular structured/unstructured meshes for the 2D model. The coupling strategies, free of hydraulic structures and tuning parameters, are firstly validated in a laboratory test dealing with a levee break and its flooding into a lateral plane. The numerical results are compared with a fully 2D model as well as with measurements in some gauge points giving satisfactory results. The simulation of a real flooding scenario in the Tiber river near the urban area of Rome (Italy) is then performed. A lateral coupling configuration is provided, in which the flood wave propagation in the main channel is simulated by means of a 1D model and the inundation of the riverside is simulated by means of a 2D model. On the other hand, a frontal coupling, in which the flood wave is simulated in a 1D model first and then it is propagated into a 2D model, is also performed. The flooding extension is almost well captured by all the schemes presented, being the 1Dâ€?D lateral configuration the most confident with speed-ups of around 15x. "}
2015
- A. Lacasta, M. Morales-Hernández, M. Tejero-Juste, J. Burguete, P. Brufau, and P. GarcÃa-Navarro, "Calibración y simulación de un sistema regulado de suministro de agua a través de técnicas de monte carlo," IngenierÃa del agua, vol. 19, iss. 3, p. 117–133, 2015.
[Bibtex]@article{lacasta2015calibracion,title = {Calibración y simulación de un sistema regulado de suministro de agua a través de técnicas de Monte Carlo},author={Lacasta, A and Morales-Hernández, M and Tejero-Juste, M and Burguete, J and Brufau, P and GarcÃa-Navarro, P},journal={IngenierÃa del agua},volume={19},number={3},issn = {1886-4996}, pages = {117--133}, doi = {10.4995/ia.2015.3350},year={2015},keywords = {Simulación Hidráulica; Flujo en Superficie Libre; Monte Carlo; Calibración; Ecuaciones de Aguas Poco Profundas},abstract = {El flujo en canales se caracteriza por cubrir largas distancias y obedecer a patrones temporales variables. Suele estar regulado por elementos hidráulicos, como compuertas laterales, para asegurar un correcto abastecimiento de agua. La dinámica de este flujo viene gobernada por un sistema de ecuaciones diferenciales en derivadas parciales llamado de aguas poco profundas. Junto a ellas es necesario establecer una formulación simplificada del funcionamiento de las compuertas. El conjunto forma un sistema no lineal que sólo se puede resolver numéricamente. Aquà se propone un esquema descentrado explÃcito de volúmenes finitos con el fin de resolver todo tipo de regÃmenes. La modelización de las estructuras hidráulicas (compuertas laterales) introduce parámetros con incertidumbre. Por ello, serán calibradas mediante el algoritmo de Monte Carlo, obteniendo como resultado unos coeficientes asociados a cada una de ellas. Posteriormente serán verificadas utilizando casos reales proporcionados por el equipo de monitorización del canal de Pina de Ebro (Zaragoza).},url = {http://polipapers.upv.es/index.php/IA/article/view/3350}} - A. Navas-Montilla and J. Murillo, "Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations," Journal of computational physics, vol. 290, pp. 188-218, 2015.
[Bibtex]@article{NavasMontilla2015188,title = "Energy balanced numerical schemes with very high order. {T}he {A}ugmented {R}oe {F}lux {ADER} scheme. {A}pplication to the shallow water equations ",journal = "Journal of Computational Physics ",volume = "290",number = "",pages = "188 - 218",year = "2015",note = "",issn = "0021-9991",doi = "10.1016/j.jcp.2015.03.002",url = "http://www.sciencedirect.com/science/article/pii/S0021999115001217",author = "A. Navas-Montilla and J. Murillo",keywords = "ADER",keywords = "Well balanced",keywords = "Energy balanced",keywords = "Roe solver",keywords = "Burgers",keywords = "Shallow water",keywords = "High order accuracy ",abstract = "Abstract In this work, an \{ADER\} type finite volume numerical scheme is proposed as an extension of a first order solver based on weak solutions of \{RPs\} with source terms. The type of source terms considered here are a special but relevant type of source terms: their spatial integral is discontinuous. The relevant difference with other previously defined \{ADER\} schemes is that it considers the presence of the source term in the solutions of the DRP. Unlike the original \{ADER\} schemes, the proposed numerical scheme computes the \{RPs\} of the high order terms of the \{DRP\} departing from time derivatives of the fluxes as initial conditions for these RPs. Weak solutions of the \{RPs\} defined for the \{DRP\} are computed using an augmented version of the Roe solver that includes an extra wave that accounts for the contribution of the source term. The discretization done over the source term leads to an energy balanced numerical scheme that allows to obtain the exact solution for steady cases with independence of the grid refinement. In unsteady problems, the numerical scheme ensures the convergence to the exact solution. The numerical scheme is constructed with an arbitrary order of accuracy, and has no theoretical barrier. Numerical results for the Burger's equation and the shallow water equations are presented in this work and indicate that the proposed numerical scheme is able to converge with the expected order of accuracy. "} - A. Lacasta, M. Morales-Hernández, J. Murillo, and P. GarcÃa-Navarro, "GPU implementation of the 2D shallow water equations for the simulation of rainfall/runoff events," Environmental earth sciences, vol. 74, iss. 11, pp. 7295-7305, 2015.
[Bibtex]@article{alacastagpuhydro,year={2015},issn={1866-6280},journal={Environmental Earth Sciences},volume={74},number={11},doi={10.1007/s12665-015-4215-z},title={{GPU} implementation of the {2D} shallow water equations for the simulation of rainfall/runoff events},url={http://dx.doi.org/10.1007/s12665-015-4215-z},publisher={Springer Berlin Heidelberg},keywords={Shallow water equations; GPU; Unstructured meshes; Rainfall/runoff; Wet/dry cells},author={Lacasta, Asier and Morales-Hernández, Mario and Murillo, Javier and GarcÃa-Navarro, Pilar},pages={7295-7305},language={English}} - M. Morales-Hernández, A. Lacasta, J. Murillo, P. Brufau, and P. GarcÃa-Navarro, "A Riemann coupled edge (RCE) 1D??D finite volume inundation and solute transport model," Environmental earth sciences, vol. 74, iss. 11, pp. 7319-7335, 2015.
[Bibtex]@article{MoralesHernandezRCE1D2D,year={2015},issn={1866-6280},journal={Environmental Earth Sciences},volume={74},number={11},doi={10.1007/s12665-015-4754-3},title={A {R}iemann coupled edge ({RCE}) 1{D}â€?{D} finite volume inundation and solute transport model},url={http://dx.doi.org/10.1007/s12665-015-4754-3},publisher={Springer Berlin Heidelberg},keywords={1Dâ€?D coupled model; Shallow water; Conservation; Solute transport; Riemann problem},author={Morales-Hernández, M. and Lacasta, A. and Murillo, J. and Brufau, P. and GarcÃa-Navarro, P.},pages={7319-7335},language={English}} - A. Lacasta, C. Juez, J. Murillo, and P. Garcia-Navarro, "An efficient solution for hazardous geophysical flows simulation using GPUs," Computers & geosciences, vol. 78, pp. 63-72, 2015.
[Bibtex]@article{Lacasta201563,title = "An efficient solution for hazardous geophysical flows simulation using {GPU}s",journal = "Computers & Geosciences ",volume = "78",number = "0",pages = "63 - 72",year = "2015",note = "",issn = "0098-3004",doi = "10.1016/j.cageo.2015.02.010",url = "http://www.sciencedirect.com/science/article/pii/S0098300415000321",author = "A. Lacasta and C. Juez and J. Murillo and P. Garcia-Navarro",keywords = "\{CUDA\}",keywords = "\{GPU\}",keywords = "Landslides",keywords = "Numerical modeling",keywords = "Shallow flow",keywords = "Coulomb forces ",abstract = "Abstract The movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the understanding and predictions of such landslides. The main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in the calculus. In order to overcome this problem, this work proposes the use of \{GPUs\} for decreasing significantly the \{CPU\} simulation time. The numerical scheme implemented in \{GPU\} is based on a finite volume scheme and it was validated in previous work with exact solutions and experimental data. The computational cost time obtained with the Graphical Hardware technology, GPU, is compared against Single-Core (sequential) and Multi-Core (parallel) \{CPU\} implementations. The \{GPU\} implementation allows to reduce the computational cost time in two orders of magnitude. "} - J. Murillo and P. Garcia-Navarro, "A Roe type energy balanced solver for 1D arterial blood flow and transport," Computers & fluids, vol. 117, pp. 149-167, 2015.
[Bibtex]@article{Murillo2015149,title = "A {R}oe type energy balanced solver for 1{D} arterial blood flow and transport ",journal = "Computers & Fluids ",volume = "117",number = "0",pages = "149 - 167",year = "2015",note = "",issn = "0045-7930",doi = "10.1016/j.compfluid.2015.05.003",url = "http://www.sciencedirect.com/science/article/pii/S0045793015001504",author = "J. Murillo and P. Garcia-Navarro",keywords = "Energy-balanced",keywords = "Well-balanced",keywords = "Roe",keywords = "Arteries",keywords = "Networks",keywords = "Transport ",abstract = "Abstract The approximate solver presented in this work is based on the upwind discretization of the source terms and a genuinely Roe solver for the one-dimensional blood flow equations in arteries. This augmented solver involves the presence of the source terms, ensuring convergence to the exact solution by including an extra wave associated to the change in the material properties and the friction term. The resulting numerical scheme is energy-balanced, that is, ensures equilibrium in rest conditions and is able to ensure numerically a constant level of energy in steady cases with velocity. The resulting numerical solver allows simulating directly mass transport without creating non-physical oscillations. The numerical scheme is assessed using steady and unsteady problems with exact solutions and is compared with models of the systemic arterial tree published in literature. "} - M. González-Sanchis, J. Murillo, A. Cabezas, J. E. Vermaat, F. A. Comin, and P. Garcia-Navarro, "Modelling sediment deposition and phosphorus retention in a river floodplain," Hydrological processes, vol. 29, iss. 3, pp. 384-394, 2015.
[Bibtex]@article {HYP:HYP10152,author = {González-Sanchis, M. and Murillo, J. and Cabezas, A. and Vermaat, J. E. and Comin, F. A. and Garcia-Navarro, P.},title = {Modelling sediment deposition and phosphorus retention in a river floodplain},journal = {Hydrological Processes},volume = {29},number = {3},issn = {1099-1085},url = {http://dx.doi.org/10.1002/hyp.10152},doi = {10.1002/hyp.10152},pages = {384-394},keywords = {phosphorus retention, model validation, sediment deposition, floodplain, numerical modelling},year = {2015},abstract = {Phosphorus (P) is one of the major limiting nutrient in many freshwater ecosystems. During the last decade, attention has been focused on the fluxes of suspended sediment and particulate P through freshwater drainage systems because of severe eutrophication effects in aquatic ecosystems. Hence, the analysis and prediction of phosphorus and sediment dynamics constitute an important element for ecological conservation and restoration of freshwater ecosystems. In that sense, the development of a suitable prediction model is justified, and the present work is devoted to the validation and application of a predictive soluble reactive phosphorus (SRP) uptake and sedimentation models, to a real riparian system of the middle Ebro river floodplain. Both models are coupled to a fully distributed two-dimensional shallow-water flow numerical model. The SRP uptake model is validated using data from three field experiments. The model predictions show a good accuracy for SRP concentration, where the linear regressions between measured and calculated values of the three experiments were significant (r2 ≥�.62; p ≤�.05), and a Nash–Sutcliffe coefficient (E) that ranged from 0.54 to 0.62. The sedimentation model is validated using field data collected during two real flooding events within the same river reach. The comparison between calculated and measured sediment depositions showed a significant linear regression (p ≤�.05; r2��.97) and an E that ranged from 0.63 to 0.78. Subsequently, the complete model that includes flow dynamics, solute transport, SRP uptake and sedimentation is used to simulate and analyse floodplain sediment deposition, river nutrient contribution and SRP uptake. According to this analysis, the main SRP uptake process appears to be the sediment sorption. The analysis also reveals the presence of a lateral gradient of hydrological connectivity that decreases with distance from the river and controls the river matter contribution to the floodplain. Copyright © 2014 John Wiley & Sons, Ltd.},}
2014
- D. Caviedes-Voullième, C. Juez, J. Murillo, and P. GarcÃa-Navarro, "2D dry granular free-surface flow over complex topography with obstacles. part i: experimental study using a consumer-grade rgb-d sensor," Computers & geosciences, vol. 73, pp. 177-197, 2014.
[Bibtex]@article{CaviedesVoullième2014177,title = "2{D} dry granular free-surface flow over complex topography with obstacles. Part I: experimental study using a consumer-grade RGB-D sensor ",journal = "Computers & Geosciences ",volume = "73",number = "0",pages = "177 - 197",year = "2014",note = "",issn = "0098-3004",doi = "10.1016/j.cageo.2014.09.009",url = "http://www.sciencedirect.com/science/article/pii/S0098300414002210",author = "Daniel Caviedes-Voullième and Carmelo Juez and Javier Murillo and Pilar GarcÃa-Navarro",keywords = "Granular flow",keywords = "Avalanches",keywords = "3D sensing device",keywords = "RGB-D sensor",keywords = "Complex topography ",abstract = "Abstract Avalanches, debris flows and other types of gravity-driven granular flows are a common hazard in mountainous regions. These regions often have human settlements in the lower parts of valleys, with human structures dangerously exposed to the destructive effects of these geophysical flows. Therefore a scientific effort has been made to understand, model and simulate geophysical granular flows. In order for computer models and simulations to be of predictive value they need to be validated under controlled, yet nature-like conditions. This work presents an experimental study of granular flow over a simplified mountain slope and valley topography. The experimental facility has a rough bed with very high slope at the upstream end and adverse slope on the downstream end, following a parabolic profile. Obstacles are present in the lower regions. Transient measurements of the moving granular surfaces were taken with a consumer-grade RGB-D sensor, providing transient 2{D} elevation fields around the obstacles. Three experimental configurations were tested, with semispheres of different diameters and a square dike obstacle. The experimental results are very consistent and repeatable. The quantitative, transient and two-dimensional data for all three experiments constitute excellent benchmarking tests for computational models, such as the one presented in a companion paper. "} - C. Juez, D. Caviedes-Voullième, J. Murillo, and P. GarcÃa-Navarro, "2D dry granular free-surface transient flow over complex topography with obstacles. part ii: numerical predictions of fluid structures and benchmarking," Computers & geosciences, vol. 73, pp. 142-163, 2014.
[Bibtex]@article{Juez2014142,title = "2{D} dry granular free-surface transient flow over complex topography with obstacles. Part II: Numerical predictions of fluid structures and benchmarking ",journal = "Computers & Geosciences ",volume = "73",number = "0",pages = "142 - 163",year = "2014",note = "",issn = "0098-3004",doi = "10.1016/j.cageo.2014.09.010",url = "http://www.sciencedirect.com/science/article/pii/S0098300414002222",author = "C. Juez and D. Caviedes-Voullième and J. Murillo and P. GarcÃa-Navarro",keywords = "Granular flow",keywords = "Landslides",keywords = "Numerical modeling",keywords = "Obstacles ",abstract = "Abstract Dense granular flows are present in geophysics and in several industrial processes, which has lead to an increasing interest for the knowledge and understanding of the physics which govern their propagation. For this reason, a wide range of laboratory experiments on gravity-driven flows have been carried out during the last two decades. The present work is focused on geomorphological processes and, following previous work, a series of laboratory studies which constitute a further step in mimicking natural phenomena are described and simulated. Three situations are considered with some common properties: a two-dimensional configuration, variable slope of the topography and the presence of obstacles. The setup and measurement technique employed during the development of these experiments are deeply explained in the companion work. The first experiment is based on a single obstacle, the second one is performed against multiple obstacles and the third one studies the influence of a dike on which overtopping occurs. Due to the impact of the flow against the obstacles, fast moving shocks appear, and a variety of secondary waves emerge. In order to delve into the physics of these types of phenomena, a shock-capturing numerical scheme is used to simulate the cases. The suitability of the mathematical models employed in this work has been previously validated. Comparisons between computed and experimental data are presented for the three cases. The computed results show that the numerical tool is able to predict faithfully the overall behavior of this type of complex dense granular flow. "} - A. Lacasta, M. Morales-Hernández, J. Murillo, and P. GarcÃa-Navarro, "An optimized \GPU\ implementation of a 2D free surface simulation model on unstructured meshes," Advances in engineering software, vol. 78, pp. 1-15, 2014.
[Bibtex]@article{Lacasta20141,title = "An optimized \{GPU\} implementation of a 2{D} free surface simulation model on unstructured meshes ",journal = "Advances in Engineering Software ",volume = "78",number = "0",pages = "1 - 15",year = "2014",note = "",issn = "0965-9978",doi = "10.1016/j.advengsoft.2014.08.007",url = "http://www.sciencedirect.com/science/article/pii/S0965997814001331",author = "A. Lacasta and M. Morales-Hernández and J. Murillo and P. GarcÃa-Navarro",keywords = "\{GPU\}",keywords = "Finite volume methods",keywords = "Unsteady flow",keywords = "Unstructured meshes",keywords = "Dry/wet boundaries",keywords = "\{CUDA\}",keywords = "High performance computing ",abstract = "Abstract This work is related with the implementation of a finite volume method to solve the 2D Shallow Water Equations on Graphic Processing Units (GPU). The strategy is fully oriented to work efficiently with unstructured meshes which are widely used in many fields of Engineering. Due to the design of the \{GPU\} cards, structured meshes are better suited to work with than unstructured meshes. In order to overcome this situation, some strategies are proposed and analyzed in terms of computational gain, by means of introducing certain ordering on the unstructured meshes. The necessity of performing the simulations using unstructured instead of structured meshes is also justified by means of some test cases with analytical solution. "} - D. Caviedes-Voullième, M. Morales-Hernández, I. López-Marijuan, and P. GarcÃa-Navarro, "Reconstruction of 2D river beds by appropriate interpolation of 1D cross-sectional information for flood simulation," Environmental modelling & software, vol. 61, pp. 206-228, 2014.
[Bibtex]@article{CaviedesVoullième2014206,title = "Reconstruction of 2{D} river beds by appropriate interpolation of 1{D} cross-sectional information for flood simulation ",journal = "Environmental Modelling & Software ",volume = "61",number = "0",pages = "206 - 228",year = "2014",note = "",issn = "1364-8152",doi = "10.1016/j.envsoft.2014.07.016",url = "http://www.sciencedirect.com/science/article/pii/S1364815214002308",author = "Daniel Caviedes-Voullième and Mario Morales-Hernández and Ibai López-Marijuan and Pilar GarcÃa-Navarro",keywords = "River bed bathymetry",keywords = "Digital terrain model",keywords = "River flow simulation",keywords = "2D shallow water equations ",abstract = "Abstract The 2D numerical simulation of river flow requires a large amount of topographic data to build an accurate Digital Terrain Model which must cover the main river channel and the area likely to be flooded. \{DTMs\} for large floodplains are often generated by LiDAR flights. However, it is often impossible to obtain LiDAR data of permanently inundated river beds. These areas are often surveyed and discrete cross-sections of the river channel are obtained. This work presents an algorithm to generate the missing information for the areas between cross-sections. The algorithm allows to generate a river bed which preserves important morphological features such as meanders and thalweg trajectory. Two benchmark cases are studied: a synthetic river-floodplain system and a real case application on a reach of the Ebro river in Spain. The cases are analyzed from a geometry and hydrodynamics perspective by performing 2D simulations with good results. "} - C. Juez, J. Murillo, and P. GarcÃa-Navarro, "A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed," Advances in water resources, vol. 71, pp. 93-109, 2014.
[Bibtex]@article{Juez201493,title = "A 2{D} weakly-coupled and efficient numerical model for transient shallow flow and movable bed ",journal = "Advances in Water Resources ",volume = "71",number = "0",pages = "93 - 109",year = "2014",note = "",issn = "0309-1708",doi = "10.1016/j.advwatres.2014.05.014",url = "http://www.sciencedirect.com/science/article/pii/S0309170814001080",author = "C. Juez and J. Murillo and P. GarcÃa-Navarro",keywords = "Finite volume method",keywords = "2D shallow water",keywords = "Bed load sediment transport",keywords = "Exner equation ",abstract = "Abstract Recent advances in the simulation of free surface flows over mobile bed have shown that accurate and stable results in realistic problems can be provided if an appropriate coupling between the shallow water equations (SWE) and the Exner equation is performed. This coupling can be done if using a suitable Jacobian matrix. As a result, faithful numerical predictions are available for a wide range of flow conditions and empirical bed load discharge formulations, allowing to investigate the best option in each case study, which is mandatory in these type of environmental problems. When coupling the equations, the \{SWE\} are considered but including an extra conservation law for the sediment dynamics. In this way the computational cost may become unrealistic in situations where the application of the \{SWE\} over rigid bed can be used involving large time and space scales without giving up to the adequate level of mesh refinement. Therefore, for restoring the numerical efficiency, the coupling technique is simplified, not decreasing the number of waves involved in the Riemann problem but simplifying their definitions. The effects of the approximations made are tested against experimental data which include transient problems over erodible bed. The simplified model is formulated under a general framework able to insert any desirable discharge solid load formula. "} - H. Ratia, J. Murillo, and P. GarcÃa-Navarro, "Numerical modelling of bridges in 2D shallow water flow simulations," International journal for numerical methods in fluids, vol. 75, iss. 4, p. 250–272, 2014.
[Bibtex]@article {FLD:FLD3892,author = {Ratia, H. and Murillo, J. and GarcÃa-Navarro, P.},title = {Numerical modelling of bridges in 2{D} shallow water flow simulations},journal = {International Journal for Numerical Methods in Fluids},volume = {75},number = {4},issn = {1097-0363},url = {http://dx.doi.org/10.1002/fld.3892},doi = {10.1002/fld.3892},pages = {250--272},keywords = {bridges, 2D shallow water, numerical modeling, hydraulic structures, upwind discretization},year = {2014},abstract = {Two representations of bridges are presented to fit into simulations based on the 2D SWEs. They include a novel and simple empirical formulation for total head loss caused by bridges which covers all flow regimes: free water surface, partially submerged flow, and fully submerged flow. The performances of the different representations of bridges are assessed using experimental results of steady and unsteady flows, presented for the first time in this work. A case study of a real flood is presented giving insight into the application of the representation techniques to real engineering problems. The proposed solution of a head loss representation together with the novel formulation is shown to be accurate for both steady and unsteady flows, and to perform efficiently for solving the flood case. Copyright © 2014 John Wiley & Sons, Ltd.},} - J. Burguete, A. Lacasta, and P. GarcÃa-Navarro, "Surcos: a software tool to simulate irrigation and fertigation in isolated furrows and furrow networks," Computers and electronics in agriculture, vol. 103, pp. 91-103, 2014.
[Bibtex]@article{Burguete201491,title = "SURCOS: A software tool to simulate irrigation and fertigation in isolated furrows and furrow networks ",journal = "Computers and Electronics in Agriculture ",volume = "103",number = "0",pages = "91 - 103",year = "2014",note = "",issn = "0168-1699",doi = "10.1016/j.compag.2014.02.004",url = "http://www.sciencedirect.com/science/article/pii/S0168169914000398",author = "J. Burguete and A. Lacasta and P. GarcÃa-Navarro",keywords = "Simulation software",keywords = "Infiltration",keywords = "Furrows",keywords = "Irrigation",keywords = "Fertigation ",abstract = "Abstract A software tool useful for the numerical computation of surface irrigation and fertigation in furrows and furrow networks was developed. The model solves the complete one-dimensional St-Venant equations together with the transport equation of a passive solute. The flow equations and the solute advection are solved with a high resolution \{TVD\} explicit Eulerian scheme. The solute dispersion is solved with a centered implicit Eulerian scheme to avoid further restriction in the allowable time step. The computational speed of the model is high in isolated furrows. In cases of large furrow networks over extended irrigation times the model is slower but affordable computational speed is achieved. The computational model has been designed to be robust, intuitive and able to supply useful visual results. Both the executable and the source code, as well as the examples presented can be downloaded, edited and distributed under a \{BSD\} type license. "} - A. Lacasta, M. Morales-Hernández, P. Brufau, and P. GarcÃa-Navarro, "Simulation of \PID\ control applied to irrigation channels," Procedia engineering, vol. 70, pp. 978-987, 2014.
[Bibtex]@article{Lacasta2014978,title = "Simulation of \{PID\} Control Applied to Irrigation Channels ",journal = "Procedia Engineering ",volume = "70",number = "0",pages = "978 - 987",year = "2014",note = "12th International Conference on Computing and Control for the Water Industry, \{CCWI2013\} ",issn = "1877-7058",doi = "10.1016/j.proeng.2014.02.109",url = "http://www.sciencedirect.com/science/article/pii/S1877705814001118",author = "A. Lacasta and M. Morales-Hernández and P. Brufau and P. GarcÃa-Navarro",keywords = "\{PID\}",keywords = "Irrigation Channels",keywords = "Calibration",keywords = "Simulation",keywords = "Shallow Water Equations ",abstract = "Abstract Open-channel flow usually includes many hydraulic elements to help with the regulation of water supply in terms of automatic control. On the other hand, the one-dimensional Shallow Water Equations (SWE) are widely used to model and predict the flow dynamics in this kind of configurations. In this work, the unsteady \{SWE\} are used to model the water motion and they are solved using a finite volume upwind scheme able to cope with all flow regimes. Furthermore, the regulation of hydraulic structures at channels is frequently based on the \{PID\} controller. In this work, the implementation and coupling of the channel flow simulation with hydraulic elements and \{PID\} regulation is performed. "} - J. Fernández-Pato and P. GarcÃa-Navarro, "A pipe network simulation model with dynamic transition between free surface and pressurized flow," Procedia engineering, vol. 70, pp. 641-650, 2014.
[Bibtex]@article{FernándezPato2014641,title = "A Pipe Network Simulation Model with Dynamic Transition between Free Surface and Pressurized Flow ",journal = "Procedia Engineering ",volume = "70",number = "0",pages = "641 - 650",year = "2014",note = "12th International Conference on Computing and Control for the Water Industry, \{CCWI2013\} ",issn = "1877-7058",doi = "10.1016/j.proeng.2014.02.070",url = "http://www.sciencedirect.com/science/article/pii/S1877705814000721",author = "J. Fernández-Pato and P. GarcÃa-Navarro",keywords = "Shallow water flow",keywords = "pressurized flow",keywords = "pipe network",keywords = "Preissmann slot",keywords = "transitory",keywords = "stationary",keywords = "finite volume",keywords = "Roe scheme",keywords = "upwind",keywords = "water hammer ",abstract = "Abstract Water flow numerical simulation in urban sewer systems is a topic that combines surface flows and pressurized flows in steady and transient situations. A numerical simulation model is developed in this work, capable of solving pipe networks mainly unpressur- ized, with isolated peaks of pressurization. For this purpose, a reformulation of the mathematical model through the Preissmann slot method is proposed. The numerical model is based on the first order Roe's scheme, in the frame of finite volume methods. The validation has been done by means of several cases with analytic solutions or empirical laboratory data. "} - J. Fernández-Pato and P. GarcÃa-Navarro, "Finite volume simulation of unsteady water pipe flow," Drinking water engineering and science, vol. 7, pp. 83-92, 2014.
[Bibtex]@article{FernándezPatoDWES,title = "Finite volume simulation of unsteady water pipe flow ",journal = "Drinking Water Engineering and Science",volume = "7",number = "0",pages = "83 - 92",year = "2014",doi = "doi:10.5194/dwes-7-83-2014",url = "http://www.drink-water-eng-sci.net/7/83/2014/dwes-7-83-2014.html",author = "J. Fernández-Pato and P. GarcÃa-Navarro",keywords = "Shallow water flow",keywords = "pressurized flow",keywords = "pipe network",keywords = "Preissmann slot",keywords = "transitory",keywords = "stationary",keywords = "finite volume",keywords = "Roe scheme",keywords = "upwind",abstract = "The most commonly used hydraulic network models used in the drinking water community exclusively consider fully filled pipes. However, water flow numerical simulation in urban pipe systems may require to model transitions between surface flow and pressurized flow in steady and transient situations. The governing equations for both flow types are different and this must be taken into account in order to get a complete numerical model for solving dynamically transients. In this work, a numerical simulation tool is developed, capable of simulating pipe networks mainly unpressurized, with isolated points of pressurization. For this purpose, the mathematical model is reformulated by means of the Preissmann slot method. This technique provides a reasonable estimation of the water pressure in cases of pressurization. The numerical model is based on the first order Roe's scheme, in the frame of finite volume methods. The novelty of the method is that it is adapted to abrupt transient situations, with subcritical and supercritical flows. The validation has been done by means of several cases with analytic solutions or empirical laboratory data. It has also been applied to some more complex and realistic cases, like junctions or pipe networks. "} - M. Morales-Hernandez, M. E. Hubbard, and P. Garcia-Navarro, "A 2D extension of a large time step explicit scheme (CFL > 1) for unsteady problems with wet/dry boundaries," Journal of computational physics, vol. 263, pp. 303-327, 2014.
[Bibtex]@article{Morales,author = {Morales-Hernandez, M. and Hubbard, M.E. and Garcia-Navarro, P.},title = {A 2{D} extension of a Large Time Step explicit scheme ({CFL} > 1) for unsteady problems with wet/dry boundaries},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {263},doi = {10.1016/j.jcp.2014.01.019},pages = {303-327},year = {2014},abstract = {A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1{D} case related to source terms, boundary conditions and the reduction of the time step in the presence of large discontinuities. The boundary conditions treatment as well as the wet/dry fronts in the case of the 2D shallow water equations require extra effort. The proposed scheme is tested on linear and non-linear equations and systems, with and without source terms. The numerical results are compared with those of the conventional scheme as well as with analytical solutions and experimental data.}} - J. Murillo and P. Garcia-Navarro, "Accurate numerical modeling of 1d flow in channels with arbitrary shape. application of the energy balanced property," Journal of computational physics, vol. 260, pp. 222-248, 2014.
[Bibtex]@article{Murillo,author = {Murillo, J. and Garcia-Navarro, P.},title = {Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {260},doi = {10.1016/j.jcp.2013.12.040},pages = {222-248},year = {2014},abstract = {This work focuses on the numerical treatment of 1{D} flow in channels with arbitrary shape using energy balanced arguments. The system of equations is defined using the mass and momentum conservation equations, allowing the resolution of hydraulic jumps where energy conservation arguments are not valid. When necessary, conservation of mechanical energy takes part actively in the numerical scheme when evaluating the source terms. The numerical scheme is based on an augmented Roe solver that involves the presence of source terms by adding an extra stationary wave. The characteristics of the numerical scheme include the energy balanced property, and being only first order accurate in time and space, leads to exact numerical solutions for steady solutions with independence of the grid refinement in channels with general geometries. Riemann problems considered here involve non-prismatic channels, bed variations and the resonance regime, including the limiting situation when the Riemann data belong to the resonance hypersurface. Numerical results point out that the finite volume numerical scheme with nonconservative terms presented here, converges to the exact solution. The well balanced property is ensured, as it is a particular case of the energy balanced property in cases of quiescent equilibrium.}}
2013
- C. Juez, J. Murillo, and P. GarcÃa-Navarro, "2D simulation of granular flow over irregular steep slopes using global and local coordinates," Journal of computational physics, vol. 255, pp. 166-204, 2013.
[Bibtex]@article{Juez2013166,title = "2{D} simulation of granular flow over irregular steep slopes using global and local coordinates ",journal = "Journal of Computational Physics ",volume = "255",number = "0",pages = "166 - 204",year = "2013",note = "",issn = "0021-9991",doi = "10.1016/j.jcp.2013.08.002",url = "http://www.sciencedirect.com/science/article/pii/S0021999113005275",author = "C. Juez and J. Murillo and P. GarcÃa-Navarro",keywords = "Weak solutions",keywords = "Well-balanced approach",keywords = "Roe methods",keywords = "Mud/Debris flow",keywords = "Stability region",keywords = "Wet/dry front",keywords = "Shallow water systems",keywords = "Coulomb stress",keywords = "Stopping conditions",keywords = "Gravity components",keywords = "Local coordinates",keywords = "Global coordinates ",abstract = "Abstract In this work approximate augmented Riemann solvers are formulated providing appropriate numerical schemes for mathematical models of granular flow on irregular steep slopes. Fluxes and source terms are discretized to ensure steady state configurations including correct modeling of start/stop flow conditions, both in a global and a local system of coordinates. The weak solutions presented involve the effect of bed slope in pressure distribution and frictional effects by means of the adequate gravity acceleration components. The numerical solvers proposed are first tested against 1D cases with exact solution and then their results are compared with experimental data in order to check the suitability of the mathematical models described in this work. Comparisons between results provided when using global and local system of coordinates are presented. The obtained results point out that both the global and the local system of coordinates can be used to predict faithfully the overall behavior of the phenomena considered in this work. "} - A. Lacasta, P. GarcÃa-Navarro, J. Burguete, and J. Murillo, "Preprocess static subdomain decomposition in practical cases of 2D unsteady hydraulic simulation," Computers & fluids, vol. 80, pp. 225-232, 2013.
[Bibtex]@article{Lacasta2013225,title = "Preprocess static subdomain decomposition in practical cases of 2{D} unsteady hydraulic simulation ",journal = "Computers & Fluids ",volume = "80",number = "0",pages = "225 - 232",year = "2013",note = "Selected contributions of the 23rd International Conference on Parallel Fluid Dynamics ParCFD2011 ",issn = "0045-7930",doi = "10.1016/j.compfluid.2012.03.010",url = "http://www.sciencedirect.com/science/article/pii/S0045793012000977",author = "A. Lacasta and P. GarcÃa-Navarro and J. Burguete and J. Murillo",keywords = "Parallelization",keywords = "Computational hydraulics",keywords = "Unsteady flow",keywords = "Static domain decomposition",keywords = "Dry/wet boundaries ",abstract = "Explicit finite volume methods are frequently used and widely accepted in hydraulic models based on the shallow water approximation. The main drawback of the approach is the time step size limit imposed by the Courant–Friedrichs–Lewy numerical stability constraint. This leads to excessively long computational times in large scale cases of practical interest. At the same time, the accuracy of the numerical results is associated to the use of fine computational meshes able to achieve enough spatial resolution. Taking into account that hydraulic modelers do not have access, in general, to large computational facilities, suitable and useful parallelization techniques are required. Furthermore, if high performance computing facilities are used, it is usually necessary to provide an estimation of the requirements of computational load to cover the length of the simulation. In this work the suitability of a preprocess static subdomain decomposition is explored and presented as a promising strategy to improve the efficiency of 2D unsteady shallow water computational models over dry bed in medium scale computational facilities and, at the same time, is useful to provide a preprocess computational time estimation if large scale computational facilities are going to be used. "} - M. Morales-Hernández, J. Murillo, and P. GarcÃa-Navarro, "The formulation of internal boundary conditions in unsteady 2-d shallow water flows: application to flood regulation," Water resources research, vol. 49, iss. 1, pp. 471-487, 2013.
[Bibtex]@article {WRCR:WRCR20062,author = {Morales-Hernández, M. and Murillo, J. and GarcÃa-Navarro, P.},title = {The formulation of internal boundary conditions in unsteady 2-D shallow water flows: Application to flood regulation},journal = {Water Resources Research},volume = {49},number = {1},issn = {1944-7973},url = {10.1002/wrcr.20062},doi = {10.1002/wrcr.20062},pages = {471-487},keywords = {Mathematical and computer modeling, gate, internal boundary conditions, 2-D finite volume, flooding, regulation},year = {2013},abstract = {This work presents a two-dimensional hydraulic model that includes gates as internal structures. The flow is modeled using the two-dimensional shallow water equations and the gates are formulated as internal boundary conditions to provide a simulation tool for water flood management. When open channel flow in a river passes through a gate, the shallow water equations are no longer valid and energy conservation laws are required. The change in the set of equations is avoided by modeling gates as a spatial discontinuity or internal boundary condition, providing an alternative algorithm to the one used in the rest of the flooded computational domain. In the first part of this work, the requirements of an adequate discretization for gate modeling are provided in the context of a finite volume numerical scheme able to handle all kind of flow regimes over complex bed topography. In the second part of this work, the formulation of the internal boundary conditions is verified by means of a test case with exact solution. A benchmark test case is then proposed as a synthetic river reach with lateral storage areas controlled by gates. Dimensional analysis is used to establish the regulation parameters influencing the attenuation of the outlet peak discharge. It is also shown that the peak outflow discharge can be reduced by coupling the present simulator with a proportional-integral-derivative regulation algorithm. Finally, a river reach of the Ebro River is simulated with a real flooding scenario.},} - C. Juez, J. Murillo, and P. Garcia-Navarro, "Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations," Journal of hydroinformatics, vol. 15, iss. 4, pp. 1234-1257, 2013.
[Bibtex]@article{Juez1,author = {Juez, C. and Murillo, J. and Garcia-Navarro, P.},title = {Numerical assessment of bed-load discharge formulations for transient flow in 1{D} and 2{D} situations},journal = {JOURNAL OF HYDROINFORMATICS},volume = {15},number = {4},doi = {10.2166/hydro.2013.153},pages = {1234-1257},year = {2013},abstract = {Two-dimensional (2D) transient flow over an erodible bed can be modelled using shallow-water equations and the Exner equation to describe the morphological evolution of the bed. Considering the fact that well-proven capacity formulae are based on one-dimensional (1D) experimental steady flows, the assessment of these empirical relations under unsteady 1D and 2D situations is important. In order to ensure the reliability of the numerical experimentation, the formulation has to be general enough to allow the use of different empirical laws. Moreover, the numerical scheme must handle correctly the coupling between the 2D shallow-water equations and the Exner equation under any condition. In this work, a finite-volume numerical scheme that includes these two main features will be exploited here in 1D and 2D laboratory test cases. The relative performances of Meyer-Peter and Ashida and Michiue, Engelund and Fredsoe, Fernandez Luque and Van Beek, Parker, Smart, Nielsen, Wong and Camenen and Larson formulations are analysed in terms of the root mean square error. A new discretization of the Smart formula is provided, leading to promising predictions of the erosion/deposition rates. The results arising from this work are useful to justify the use of an empirical sediment bed-load discharge formula among the ones studied, regardless of the hydrodynamic situation.}} - M. Morales-Hernandez, P. Garcia-Navarro, J. Burguete, and P. Brufau, "A conservative strategy to couple 1D and 2D models for shallow water flow simulation," Computers & fluids, vol. 81, pp. 26-44, 2013.
[Bibtex]@article{MoralesHernández201326,title = {A conservative strategy to couple 1{D} and 2{D} models for shallow water flow simulation},journal = {Computers & Fluids},author = {M. Morales-Hernandez and P. Garcia-Navarro and J. Burguete and P. Brufau},volume = {81},number = {0},pages = {26 - 44},year = {2013},doi = {10.1016/j.compfluid.2013.04.001},abstract = {Abstract A 1D-2D coupled numerical model is presented in this work. 1D and 2D models are formulated using a conservative upwind cell-centred finite volume scheme. The discretization is based on cross-sections for the 1D model and with triangular unstructured grid for the 2D model. The resulting element of discretization for the coupled model is analysed and two different coupling techniques based on mass conservation and mass and momentum conservation respectively are explored, considering both frontal and lateral configurations. The interaction with the boundaries in each model is highlighted and the necessity of using the appropriate strategy according to the flow regime is also justified. The coupled model is tested through academic test cases where the numerical results are compared with a fully 2D model as well as with experimental measurements in steady and unsteady scenarios. It is also applied to a real world configuration, where the flood wave propagation in the river bed is simulated by means of a 1D model and the inundation of the riverside is dealt with a 2D model. The computational gain is also analysed. }} - J. Murillo and P. Garcia-Navarro, "Energy balance numerical schemes for shallow water equations with discontinuous topography," Journal of computational physics, vol. 236, pp. 119-142, 2013.
[Bibtex]@article{ ISI:000314801500010,Author = {Murillo, J. and Garcia-Navarro, P.},Title = {Energy balance numerical schemes for shallow water equations withdiscontinuous topography},Journal = {JOURNAL OF COMPUTATIONAL PHYSICS},Year = {2013},Volume = {236},Pages = {119-142},Month = {MAR 1},Abstract = {The well-balanced property that ensures quiescent equilibrium whensolving the shallow-water equations with varying topography is extendedin this work to ensure numerically a constant level of energy in steadycases with velocity when necessary. This is done in the context ofaugmented solvers that consider in their definition the presence of adiscontinuous bed. In order to guarantee a constant energy state aproper integral approach of the bed source term is presented. Thisapproach is systematically assessed via a series of steady test casesand Riemann problems including the resonance regime. (C) 2012 ElsevierInc. All rights reserved.},DOI = {10.1016/j.jcp.2012.11.003},Keywords = {Weak solutions; Well-balanced approach; Roe solver; HLL solver; Shallowwater; Energy balance; Resonant regime; Riemann solver; Godunov-typescheme},} - D. Caviedes-Voullieme, P. Garcia-Navarro, and J. Murillo, "Verification, conservation, stability and efficiency of a finite volume method for the 1D richards equation," Journal of hydrology, vol. 480, pp. 69-84, 2013.
[Bibtex]@article{ ISI:000315008300007,Author = {Caviedes-Voullieme, D. and Garcia-Navarro, P. and Murillo, J.},Title = {Verification, conservation, stability and efficiency of a finite volumemethod for the 1{D} Richards equation},Journal = {JOURNAL OF HYDROLOGY},Year = {2013},Volume = {480},Pages = {69-84},Month = {FEB 14},Abstract = {Richards equation is a non-linear partial differential equation thatdescribes flow in porous media. To solve it, numerical methods that needto be conservative, stable, accurate and efficient, are required. Finitevolume methods have not been reported as widely as finite difference orfinite element methods. This work is focused on providing numericalresults and analysis of several finite volume schemes in one dimension.The formulation of time discretization schemes is revisited, a stabilityanalysis is performed, and analytical and experimental benchmakrs areprovided. (C) 2012 Elsevier B.V. All rights reserved.},DOI = {10.1016/j.jhydrol.2012.12.008},Keywords = {Richards equation; Variably saturated flow; Finite volume method; Gridsensitivity; Time step sensitivity; Mualem-van Genuchten soil model},}
2012
- D. Lopez-Barrera, P. Garcia-Navarro, P. Brufau, and J. Burguete, "Diffusive-wave based hydrologic-hydraulic model with sediment transport. i: model development," Journal of hydrologic engineering, vol. 17, iss. 10, pp. 1093-1104, 2012.
[Bibtex]@article{ ISI:000312711400004,Author = {Lopez-Barrera, D. and Garcia-Navarro, P. and Brufau, P. and Burguete, J.},Title = {Diffusive-Wave Based Hydrologic-Hydraulic Model with Sediment Transport.I: Model Development},Journal = {JOURNAL OF HYDROLOGIC ENGINEERING},Year = {2012},Volume = {17},Number = {10},Pages = {1093-1104},Month = {OCT},Abstract = {In this paper, a distributed numerical model is proposed on the basis of(1) a hydrologic model for the water exchange laws; (2) a surface runoffmodel based on a hybrid two-dimensional (2D) diffusive/kinematic waveapproximation able to calculate flow over all kinds of wet/dry groundsurface slopes; (3) a groundwater flow model based on the 2D Darcy lawfor both saturated and partly saturated zones; (4) a 2D hillslopeerosion model for the sediment transport; and (5) a explicitfinite-volume discretization with specific schemes according to thecharacteristics of the flow equations, upwind for the hyperbolicequations and centered for the parabolic equations. The resulting modeloffers a variable time step, ensuring numerical stability with the timestep size sensitive to the grid cell size in the diffusive wave case andan entropy correction of the upwind fluxes to ensure conservativesolutions near local maxima in the slopes controlling the watermovement. The validation and practical application of the model ispresented in Paper II, in which the potential usefulness of the proposedmodel is demonstrated. DOI: 10.1061/(ASCE)HE.1943-5584.0000552. (C) 2012American Society of Civil Engineers.},DOI = {10.1061/(ASCE)HE.1943-5584.0000552},Keywords = {Kinematic-wave; Diffusive-wave; Noninertia-wave; Finite volumes; Upwindschemes; Hillslope erosion model; Hydrologic model; Hydraulic model},} - D. Lopez-Barrera, P. Garcia-Navarro, P. Brufau, and J. Burguete, "Diffusive-wave based hydrologic-hydraulic model with sediment transport. ii: validation and practical application," Journal of hydrologic engineering, vol. 17, iss. 10, pp. 1105-1122, 2012.
[Bibtex]@article{ ISI:000312711400005,Author = {Lopez-Barrera, D. and Garcia-Navarro, P. and Brufau, P. and Burguete, J.},Title = {Diffusive-Wave Based Hydrologic-Hydraulic Model with Sediment Transport.II: Validation and Practical Application},Journal = {JOURNAL OF HYDROLOGIC ENGINEERING},Year = {2012},Volume = {17},Number = {10},Pages = {1105-1122},Month = {OCT},Abstract = {The development of a distributed two-dimensional (2D)hydrologic-hydraulic simulation model was presented in Paper I. Thesimulation model combined overland flow (kinematic/diffusive wavemodels), hillslope sediment transport, and groundwater flow apart fromthe water exchange mechanisms between zones. Particular attention waspaid to the upwind discretization of the surface flow equations. In thispaper, the proposed model is validated by using four test cases withexact solutions, one academic test case, and two laboratory test cases.The model adequately reproduced front advance over dry beds of any slopeand water table evolution in simple cases. As practical application ofthe model, the simulation of real events in two experimental basins isalso presented. The work is focused on the influence of the choice ofthe empirical parameters on the model results concerning solid andliquid discharges. Also, because of the lack of information referringthe boundary and initial conditions of the groundwater flow in realbasins, it is difficult to evaluate the accuracy of the complete model.DOI: 10.1061/(ASCE)HE.1943-5584.0000551. (C) 2012 American Society ofCivil Engineers.},DOI = {10.1061/(ASCE)HE.1943-5584.0000551},Keywords = {Kinematic-wave; Diffusive-wave; Noninertia-wave; Finite volumes; Upwindschemes; Hillslope erosion model; Hydrologic model; Hydraulic model},} - J. Murillo and P. Garcia-Navarro, "Augmented versions of the hll and hllc riemann solvers including source terms in one and two dimensions for shallow flow applications," Journal of computational physics, vol. 231, iss. 20, pp. 6861-6906, 2012.
[Bibtex]@article{ ISI:000307299400015,Author = {Murillo, J. and Garcia-Navarro, P.},Title = {Augmented versions of the HLL and HLLC Riemann solvers including sourceterms in one and two dimensions for shallow flow applications},Journal = {JOURNAL OF COMPUTATIONAL PHYSICS},Year = {2012},Volume = {231},Number = {20},Pages = {6861-6906},Month = {AUG 15},Abstract = {Shallow water flows are found in a variety of engineering problemsalways dominated by the presence of bed friction and irregularbathymetry. These source terms determine completely the possibleevolution of the flooded area in time. It is well known that appropriatenumerical schemes for this type of flows must be well-balanced.Well-balanced numerical schemes are based on the preservation of casesof quiescent equilibrium over variable bed elevation. Commonly they areformulated as an adaptation of numerical solvers defined for caseswithout source terms. This procedure is insufficient when applied toreal situations. Then, it is possible to argue that appropriatenumerical schemes cannot arise directly from those derived from thesimplest homogeneous case without source terms. New solutions arepresented in this work by defining weak solutions that include thepresence of source terms. To do that, the solvers presented in this workextend the number of waves in the well known HLL and HLLC solversinvolving a stationary jump in the solution. This is done withoutmodifying the original solution vector of conserved quantities. Theresulting approximate Riemann solvers include variable bed level surfaceand friction. Solvers are systematically assessed via a series of testproblems with exact solutions for one and two dimensions, includingsteady and unsteady flow configurations, variation of the flooded areain time and comparisons with experimental data. The obtained resultspoint out that the new method is able to predict faithfully the overallbehavior of the solution and of any type of waves. (C) 2012 ElsevierInc. All rights reserved.},DOI = {10.1016/j.jcp.2012.06.031},Keywords = {Weak solutions; HLL; HLLC; Roe; Source terms; Augmented solver;Well-balanced approach; Stability region; Wet/dry front; Shallow water},} - M. Morales-Hernandez, P. Garcia-Navarro, and J. Murillo, "A large time step 1D upwind explicit scheme (CFL > 1): application to shallow water equations," Journal of computational physics, vol. 231, iss. 19, pp. 6532-6557, 2012.
[Bibtex]@article{ ISI:000306606900017,Author = {Morales-Hernandez, M. and Garcia-Navarro, P. and Murillo, J.},Title = {A large time step 1{D} upwind explicit scheme ({CFL} > 1): Application toshallow water equations},Journal = {JOURNAL OF COMPUTATIONAL PHYSICS},Year = {2012},Volume = {231},Number = {19},Pages = {6532-6557},Month = {AUG 1},Abstract = {It is possible to relax the Courant-Friedrichs-Lewy condition over thetime step when using explicit schemes. This method, proposed by Leveque,provides accurate and correct solutions of non-sonic shocks.Rarefactions need some adjustments which are explored in the presentwork with scalar equation and systems of equations. The non-conservativeterms that appear in systems of conservation laws introduce an extradifficulty in practical application. The way to deal with source termsis incorporated into the proposed procedure. The boundary treatment isanalysed and a reflection wave technique is considered. In presence ofstrong discontinuities or important source terms, a strategy is proposedto control the stability of the method allowing the largest time steppossible. The performance of the above scheme is evaluated to solve thehomogeneous shallow water equations and the shallow water equations withsource terms. (C) 2012 Elsevier Inc. All rights reserved.},DOI = {10.1016/j.jcp.2012.06.017},Keywords = {Large time step scheme; Hyperbolic conservation laws; Source terms;Boundary conditions; Shallow water flows; CFL limit},} - D. Caviedes-Voullieme, P. Garcia-Navarro, and J. Murillo, "Influence of mesh structure on 2D full shallow water equations and scs curve number simulation of rainfall/runoff events," Journal of hydrology, vol. 448, pp. 39-59, 2012.
[Bibtex]@article{ ISI:000306045500004,Author = {Caviedes-Voullieme, D. and Garcia-Navarro, P. and Murillo, J.},Title = {Influence of mesh structure on 2{D} full shallow water equations and SCSCurve Number simulation of rainfall/runoff events},Journal = {JOURNAL OF HYDROLOGY},Year = {2012},Volume = {448},Pages = {39-59},Month = {JUL 2},Abstract = {Hydrological simulation of rain-runoff processes is often performed withlumped models which rely on calibration to generate storm hydrographsand study catchment response to rain. In this paper, a distributed,physically-based numerical model is used for runoff simulation in amountain catchment. This approach offers two advantages. The first isthat by using shallow-water equations for runoff flow, there is lessfreedom to calibrate routing parameters (as compared to, for example,synthetic hydrograph methods). The second, is that spatial distributionsof water depth and velocity can be obtained. Furthermore, interactionsamong the various hydrological processes can be modeled in aphysically-based approach which may depend on transient and spatiallydistributed factors. On the other hand, the undertaken numericalapproach relies on accurate terrain representation and mesh selection,which also affects significantly the computational cost of thesimulations. Hence, we investigate the response of a gauged catchmentwith this distributed approach. The methodology consists of analyzingthe effects that the mesh has on the simulations by using a range ofmeshes. Next, friction is applied to the model and the response tovariations and interaction with the mesh is studied. Finally, a firstapproach with the well-known SCS Curve Number method is studied toevaluate its behavior when coupled with a shallow-water model for runoffflow. The results show that mesh selection is of great importance, sinceit may affect the results in a magnitude as large as physical factors,such as friction. Furthermore, results proved to be less sensitive toroughness spatial distribution than to mesh properties. Finally, theresults indicate that SCS-CN may not be suitable for simulatinghydrological processes together with a shallow-water model. (C) 2012Elsevier B.V. All rights reserved.},DOI = {10.1016/j.jhydrol.2012.04.006},Keywords = {Finite volumes; Shallow-water equations; Mesh generation; SCS-CN},} - M. Gonzalez-Sanchis, J. Murillo, B. Latorre, F. Comin, and P. Garcia-Navarro, "Transient two-dimensional simulation of real flood events in a mediterranean floodplain," Journal of hydraulic engineering-asce, vol. 138, iss. 7, pp. 629-641, 2012.
[Bibtex]@article{ ISI:000310148700005,Author = {Gonzalez-Sanchis, M. and Murillo, J. and Latorre, B. and Comin, F. andGarcia-Navarro, P.},Title = {Transient Two-Dimensional Simulation of Real Flood Events in aMediterranean Floodplain},Journal = {JOURNAL OF HYDRAULIC ENGINEERING-ASCE},Year = {2012},Volume = {138},Number = {7},Pages = {629-641},Month = {JUL},Abstract = {The application of a two-dimensional (2D) finite volume numerical modelto real flood events in the Ebro River is presented. The hydraulic modelused is based on the 2D transient shallow-water equations on theirregular bed that are able to compute flow advance over a dry bed. Thisstudy involves the reliable simulation of not only the flood waveadvance but also the drying process in a series of events of differentmagnitude. The importance of the correct characterization of theroughness coefficient and the topography is emphasized in the study. Theformer is estimated from a previous classification of structurallyhomogeneous habitats, and the latter is defined by merging the digitalterrain model data with a hydraulic river bed elevation reconstructionalgorithm. The calibration of the full model resulting from theroughness, bed river, and flow simulation models is based on fieldmeasurements of the flooded area for two steady discharges. Thevalidation is performed by comparing the numerical results with thewater levels measured during five flood events at certain times, withthe flooded area and time series of continuous point measurements ofwater depth during different situations throughout the year. Because themodel provides correct predictions of the surface processes both for lowand high flow discharges, the simulation results are used to analyze thepresent floodplain hydrodynamics. In the same way, different topographicscenarios, on the basis of changes in the hydraulic river-floodplainconnectivity, are generated to analyze their potentially beneficialeffect in the floodplain geomorphic dynamics. DOI:10.1061/(ASCE)HY.1943-7900.0000565. (C) 2012 American Society of CivilEngineers.},DOI = {10.1061/(ASCE)HY.1943-7900.0000565},Keywords = {Unsteady surface flow; Wetting/drying; Finite volume; Shallow water;Hydrodynamic; Floodplain; Hydraulic bed reconstruction},} - J. Murillo, B. Latorre, and P. Garcia-Navarro, "A riemann solver for unsteady computation of 2D shallow flows with variable density," Journal of computational physics, vol. 231, iss. 14, pp. 4775-4807, 2012.
[Bibtex]@article{ ISI:000304257600016,Author = {Murillo, J. and Latorre, B. and Garcia-Navarro, P.},Title = {A Riemann solver for unsteady computation of 2{D} shallow flows withvariable density},Journal = {JOURNAL OF COMPUTATIONAL PHYSICS},Year = {2012},Volume = {231},Number = {14},Pages = {4775-4807},Month = {MAY 20},Abstract = {A novel 2D numerical model for vertically homogeneous shallow flows withvariable horizontal density is presented. Density varies according tothe volumetric concentration of different components or species that canrepresent suspended material or dissolved solutes. The system ofequations is formed by the 2D equations for mass and momentum of themixture, supplemented by equations for the mass or volume fraction ofthe mixture constituents. A new formulation of the Roe-type schemeincluding density variation is defined to solve the system ontwo-dimensional meshes. By using an augmented Riemann solver, thenumerical scheme is defined properly including the presence of sourceterms involving reaction. The numerical scheme is validated usinganalytical steady-state solutions of variable-density flows and exactsolutions for the particular case of initial value Riemann problems withvariable bed level and reaction terms. Also, a 2D case that includesinteraction with obstacles illustrates the stability and robustness ofthe numerical scheme in presence of non-uniform bed topography andwetting/drying fronts. The obtained results point out that the newmethod is able to predict faithfully the overall behavior of thesolution and of any type of waves. (C) 2012 Elsevier Inc. All rightsreserved.},DOI = {10.1016/j.jcp.2012.03.016},Keywords = {Multi-component transport; Variable density; Upwind method; Solute; Weaksolutions; Well-balanced approach; Roe solver; Reactive terms; Riemannproblem; Source terms},} - J. Murillo and P. Garcia-Navarro, "Wave riemann description of friction terms in unsteady shallow flows: application to water and mud/debris floods," Journal of computational physics, vol. 231, iss. 4, pp. 1963-2001, 2012.
[Bibtex]@article{ ISI:000300462100045,Author = {Murillo, J. and Garcia-Navarro, P.},Title = {Wave Riemann description of friction terms in unsteady shallow flows:Application to water and mud/debris floods},Journal = {JOURNAL OF COMPUTATIONAL PHYSICS},Year = {2012},Volume = {231},Number = {4},Pages = {1963-2001},Month = {FEB 20},Abstract = {In this work, the source term discretization in hyperbolic conservationlaws with source terms is considered using an approximate augmentedRiemann solver. The technique is applied to the shallow water equationswith bed slope and friction terms with the focus on the frictiondiscretization. The augmented Roe approximate Riemann solver provides afamily of weak solutions for the shallow water equations, that are thebasis of the upwind treatment of the source term. This has provedsuccessful to explain and to avoid the appearance of instabilities andnegative values of the thickness of the water layer in cases of variablebottom topography. Here, this strategy is extended to capture thepeculiarities that may arise when defining more ambitious scenarios,that may include relevant stresses in cases of mud/debris flow. Theconclusions of this analysis lead to the definition of an accurate androbust first order finite volume scheme, able to handle correctlytransient problems considering frictional stresses in both clean waterand debris flow, including in this last case a correct modelling ofstopping conditions. (C) 2011 Elsevier Inc. All rights reserved.},DOI = {10.1016/j.jcp.2011.11.014},Keywords = {Weak solutions; Well-balanced approach; Roe methods; Mud/debris flow;Stability region; Wet/dry front; Shallow water systems; Turbulentstress; Dispersive stress; Coulomb stress; Yield stress; Viscous stress;Stopping conditions},} - A. Serrano-Pacheco, J. Murillo, and P. Garcia-Navarro, "Finite volumes for 2D shallow-water flow with bed-load transport on unstructured grids," Journal of hydraulic research, vol. 50, iss. 2, pp. 154-163, 2012.
[Bibtex]@article{ ISI:000305412600002,Author = {Serrano-Pacheco, Alberto and Murillo, Javier and Garcia-Navarro, Pilar},Title = {Finite volumes for 2{D} shallow-water flow with bed-load transport onunstructured grids},Journal = {JOURNAL OF HYDRAULIC RESEARCH},Year = {2012},Volume = {50},Number = {2},Pages = {154-163},Abstract = {In this work, two-dimensional (2D) bed-load transport simulations basedon the depth-averaged shallow-water equations and the Exner equation arepresented. The Exner equation is written assuming that bed-loadtransport is governed by a power law of the depth-averaged flow velocityand by a flow/sediment interaction parameter acting as a calibrationcoefficient. Uncoupled and coupled numerical resolutions of the globalproblem are considered. A Roe-type first-order upwind scheme has beenapplied as approximate Riemann solver for the discretization on 2Dunstructured meshes. The uncoupled resolution is presented as a simpleextension of a previous 2D shallow-water model. The details of the newimplementation in the coupled system problem are provided. The modelsare tested comparing with exact solutions of 2D cases as well asexperimental laboratory data.},DOI = {10.1080/00221686.2012.669142},Keywords = {Bed-load transport; Exner equation; Grass model; shallow-water system;unstructured grid},} - J. Murillo and P. GarcÃa-Navarro, "Wave riemann description of friction terms in unsteady shallow flows: application to water and mud/debris floods," Journal of computational physics, vol. 231, iss. 4, pp. 1963-2001, 2012.
[Bibtex]@article{Murillo20121963,title = "Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods ",journal = "Journal of Computational Physics ",volume = "231",number = "4",pages = "1963 - 2001",year = "2012",note = "",issn = "0021-9991",doi = "10.1016/j.jcp.2011.11.014",url = "http://www.sciencedirect.com/science/article/pii/S0021999111006693",author = "J. Murillo and P. GarcÃa-Navarro",keywords = "Weak solutions",keywords = "Well-balanced approach",keywords = "Roe methods",keywords = "Mud/debris flow",keywords = "Stability region",keywords = "Wet/dry front",keywords = "Shallow water systems",keywords = "Turbulent stress",keywords = "Dispersive stress",keywords = "Coulomb stress",keywords = "Yield stress",keywords = "Viscous stress",keywords = "Stopping conditions ",abstract = "In this work, the source term discretization in hyperbolic conservation laws with source terms is considered using an approximate augmented Riemann solver. The technique is applied to the shallow water equations with bed slope and friction terms with the focus on the friction discretization. The augmented Roe approximate Riemann solver provides a family of weak solutions for the shallow water equations, that are the basis of the upwind treatment of the source term. This has proved successful to explain and to avoid the appearance of instabilities and negative values of the thickness of the water layer in cases of variable bottom topography. Here, this strategy is extended to capture the peculiarities that may arise when defining more ambitious scenarios, that may include relevant stresses in cases of mud/debris flow. The conclusions of this analysis lead to the definition of an accurate and robust first order finite volume scheme, able to handle correctly transient problems considering frictional stresses in both clean water and debris flow, including in this last case a correct modelling of stopping conditions. "}
2011
- D. Lopez-Barrera, P. Garcia Navarro, and P. Brufau, "Sources of uncertainty in the validation of a coupled hydrological-hydraulic simulation model with sediment transport," Houille blanche-revue internationale de l eau, iss. 3, pp. 17-22, 2011.
[Bibtex]@article{ ISI:000292784000003,Author = {Lopez-Barrera, Daniel and Garcia Navarro, Pilar and Brufau, Pilar},Title = {Sources of uncertainty in the validation of a coupledhydrological-hydraulic simulation model with sediment transport},Journal = {HOUILLE BLANCHE-REVUE INTERNATIONALE DE L EAU},Year = {2011},Number = {3},Pages = {17-22},Month = {JUN},Abstract = {Arnas and Araguas are two well-instrumented basins located in theSpanish Pyrenees. Experimental data of water discharge from differentrainfall events, together with precipitation, temperature and soilhumidity have been used in order to calibrate a distributed numericalmodel of hydrological and hydraulic processes based on a two-dimensionalapproximation of the shallow water equations. The hydrological model isbased on simple but physically-based laws to calculate theevapotranspiration and the infiltration. The surface runoff is modelledby means of a 2D diffusive-wave model. Sediment transport phenomena aresimulated by means of a hillslope erosion model. All the differentialequations involved in the processes have been discretized using anexplicit scheme on quadrilateral meshes. The work is focused on theinfluence of the choice of the empirical parameters on the model resultsconcerning solid and liquid discharges.},doi = {10.1051/lhb/2011027},keywords = {Hydrological model; Hydraulic model; Finite volumes; Experimental basins},} - B. Latorre, P. Garcia-Navarro, J. Murillo, and J. Burguete, "Accurate and efficient simulation of transport in multidimensional flow," International journal for numerical methods in fluids, vol. 65, iss. 4, pp. 405-431, 2011.
[Bibtex]@article{latorre2011accurate,title={Accurate and efficient simulation of transport in multidimensional flow},author={Latorre, B and Garcia-Navarro, P and Murillo, J and Burguete, J},journal={International Journal for Numerical Methods in Fluids},volume={65},number={4},pages={405-431},year={2011},doi = {10.1002/fld.2189},Abstract = {A new numerical method to obtain high-order approximations of thesolution of the linear advection equation in multidimensional problemsis presented. The proposed conservative formulation is explicit andbased on a single updating step. Piecewise polynomial spatialdiscretization using Legendre polynomials provides the required spatialaccuracy. The updating scheme is built from the functional approximationof the exact solution of the advection equation and a direct evaluationof the resulting integrals. The numerical details for the schemes in oneand two spatial dimensions are provided and validated using a set ofnumerical experiments. Test cases have been oriented to the convergenceand the computational efficiency analysis of the schemes. Copyright (C)2009 John Wiley \& Sons, Ltd.},keywords = {high-order schemes; linear advection; multidimensional flow; CFA;computational efficiency; Legendre polynomials},} - J. Murillo and P. Garcia-Navarro, "Improved riemann solvers for complex transport in two-dimensional unsteady shallow flow," Journal of computational physics, vol. 230, iss. 19, pp. 7202-7239, 2011.
[Bibtex]@article{Murillo_2011,title = {Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow},author = {Murillo, J. and Garcia-Navarro, P.},journal = {Journal of Computational Physics},volume = {230},number = {19},pages = {7202-7239},year = {2011},doi = {10.1016/j.jcp.2011.05.022 },abstract = {The numerical solution of advection-reaction-diffusion transport problems in two-dimensional shallow water flow is split in three subproblems in order to analyze them separately. In the first part, the advection component is solved with the help of an extended Jacobian matrix for the coupled system of flow and advection conservation laws and focusing on the correct definitions of the approximate or weak solutions. Considering that one of the conserved quantities is the solute volume, nonphysical solutions for the solute concentration may appear in complex situations and a solute fix is proposed. This is formulated for first and second order schemes. In the second part of this work, the solution of problems with volumetric reaction terms is studied and the results of single-step as well as multi-step pointwise and upwind approaches are compared in order to establish their relative performance. The upwind treatment is done in 2D cases dividing cell volumes to transform reacting terms in singular source terms. The third part is concerned with the diffusion term. The focus of this part is put on the interference between numerical and physical diffusion. A simple form to estimate the magnitude of the numerical diffusion is proposed and it is shown to improve the accuracy of the results in first and second order approaches.},keywords = {Multi-component transport; Solute fix; Weak solutions; Well-balanced approach; Roe solver; HLLC solver; Diffusion correction; Upwind reactive terms}}
2010
- J. Murillo and P. Garcia-Navarro, "Weak solutions for partial differential equations with source terms: application to the shallow water equations," Journal of computational physics, vol. 229, iss. 11, pp. 4327-4368, 2010.
[Bibtex]@article{Murillo_2010b,title = {Weak solutions for partial differential equations with source terms: Application to the shallow water equations},author = {Murillo, J. and Garcia-Navarro, P.},journal = {Journal of Computational Physics},volume = {229},number = {11},pages = {4327-4368},year = {2010},doi = {10.1016/j.jcp.2010.02.016},abstract = {Weak solutions of problems with m equations with source terms are proposed using an augmented Riemann solver defined by m + 1 states instead of increasing the number of involved equations. These weak solutions use propagating jump discontinuities connecting the m + 1 states to approximate the Riemann solution. The average of the propagated waves in the computational cell leads to a reinterpretation of the Roe's approach and in the upwind treatment of the source term of Vazquez-Cendon. It is derived that the numerical scheme can not be formulated evaluating the physical flux function at the position of the initial discontinuities, as usually done in the homogeneous case. Positivity requirements over the values of the intermediate states are the only way to control the global stability of the method. Also it is shown that the definition of well-balanced equilibrium in trivial cases is not sufficient to provide correct results: it is necessary to provide discrete evaluations of the source term that ensure energy dissipating solutions when demanded. The one and two dimensional shallow water equations with source terms due to the bottom topography and friction are presented as case study. The stability region is shown to differ from the one defined for the case without source terms, and it can be derived that the appearance of negative values of the thickness of the water layer in the proximity of the wet/dry front is a particular case, of the wet/wet fronts. The consequence is a severe reduction in the magnitude of the allowable time step size if compared with the one obtained for the homogeneous case. Starting from this result, 1D and 2D numerical schemes are developed for both quadrilateral and triangular grids, enforcing conservation and positivity over the solution, allowing computationally efficient simulations by means of a reconstruction technique for the inner states of the weak solution that allows a recovery of the time step size.},keywords = {Weak solutions; Well-balanced approach; Roe methods; Energy dissipating solutions; Stability region; Wet/dry front; Shallow water systems}} - J. Murillo and P. Garcia-Navarro, "An exner-based coupled model for two-dimensional transient flow over erodible bed," Journal of computational physics, vol. 229, iss. 23, pp. 8704-8732, 2010.
[Bibtex]@article{Murillo_2010,title = {An Exner-based coupled model for two-dimensional transient flow over erodible bed},author = {Murillo, J. and Garcia-Navarro, P.},journal = {Journal of Computational Physics},volume = {229},number = {23},pages = {8704-8732},year = {2010},doi = {10.1016/j.jcp.2010.08.006},abstract = {Transient flow over erodible bed is solved in this work assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, assumed to be well formulated by means of the depth averaged shallow water equations, and the Exner equation. The Exner equation is written assuming that bed load transport is governed by a power law of the flow velocity and by a flow/sediment interaction parameter variable in time and space. The complete system is formed by four coupled partial differential equations and a genuinely Roe-type first order scheme has been used to solve it on triangular unstructured meshes. Exact solutions have been derived for the particular case of initial value Riemann problems with variable bed level and depending on particular forms of the solid discharge formula. The model, supplied with the corresponding solid transport formulae, is tested by comparing with the exact solutions. The model is validated against laboratory experimental data of different unsteady problems over erodible bed.},keywords = {Finite volume method; Shallow water; Bed load sediment transport; Exner equation; 2D weak solutions; Roe method; Bank equilibrium}}
2009
- J. Murillo, P. Garcia-Navarro, and J. Burguete, "Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow," Journal of computational physics, vol. 228, iss. 15, pp. 5539-5573, 2009.
[Bibtex]@article{Murillo_2009,title = {Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow},author = {Murillo, J. and Garcia-Navarro, P. and Burguete, J.},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {228},number = {15},pages = {5539-5573},year = {2009},doi = {10.1016/j.jcp.2009.04.039},abstract = {An explicit finite volume model to simulate two-dimensional shallow water flow with multi-component transport is presented. The governing system of coupled conservation laws demands numerical techniques to avoid unrealistic values of the transported scalars that cannot be avoided by decreasing the size of the time step. The presence of non conservative products such as bed slope and friction terms, and other source terms like diffusion and reaction, can make necessary the reduction of the time step given by the Courant number. A suitable flux difference redistribution that prevents instability and ensures conservation at all times is used to deal with the non-conservative terms and becomes necessary in cases of transient boundaries over dry bed. The resulting method belongs to the category of well-balanced Roe schemes and is able to handle steady cases with flow in motion. Test cases with exact solution, including transient boundaries, bed slope, friction, and reaction terms are used to validate the numerical scheme. Laboratory experiments are used to validate the techniques when dealing with complex systems as the kappa-epsilon model. The results of the proposed numerical schemes are compared with the ones obtained when using uncoupled formulations.},keywords = {Multi-component transport, Well-balanced approach, Reactive source terms; Shallow flow, Turbulence},} - J. Burguete, N. Zapata, P. Garcia-Navarro, M. Maikaka, E. Playan, and J. Murillo, "Fertigation in furrows and level furrow systems. i: model description and numerical tests," Journal of irrigation and drainage engineering-asce, vol. 135, iss. 4, pp. 401-412, 2009.
[Bibtex]@article{Burguete_2009,title = {Fertigation in Furrows and Level Furrow Systems. I: Model Description and Numerical Tests},author = {Burguete, J. and Zapata, N. and Garcia-Navarro, P. and Maikaka, M. and Playan, E. and Murillo, J.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {135},number = {4},pages = {401-412},year = {2009},doi = {10.1061/(ASCE)IR.1943-4774.0000097},abstract = {The simulation of fertigation in furrows and level furrow systems faces a number of problems resulting in relevant restrictions to its widespread application. In this paper, a simulation model is proposed that addresses some of these problems by: (1) implementing an infiltration model that adjusts to the variations in wetted perimeter; (2) using a friction model that adjusts to different flows and which uses an absolute roughness parameter; (3) adopting an equation for the estimation of the longitudinal diffusion coefficient; and (4) implementing a second-order TVD numerical scheme and specific treatments for the boundary conditions and the junctions. The properties of the proposed model were demonstrated using three numerical tests focusing on the numerical scheme and the treatments. The application of the model to the simulation of furrows and furrow systems is presented in a companion paper, in which the usefulness of the innovative aspects of the proposed model is demonstrated.},keywords = {},} - J. Burguete, N. Zapata, P. Garcia-Navarro, M. Maikaka, E. Playan, and J. Murillo, "Fertigation in furrows and level furrow systems. ii: field experiments, model calibration, and practical applications," Journal of irrigation and drainage engineering-asce, vol. 135, iss. 4, pp. 413-420, 2009.
[Bibtex]@article{Burguete_2009,title = {Fertigation in Furrows and Level Furrow Systems. II: Field Experiments, Model Calibration, and Practical Applications},author = {Burguete, J. and Zapata, N. and Garcia-Navarro, P. and Maikaka, M. and Playan, E. and Murillo, J.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {135},number = {4},pages = {413-420},year = {2009},doi = {10.1061/(ASCE)IR.1943-4774.0000098},abstract = {Furrow fertigation can be an interesting practice when compared to traditional overland fertilizer application. In the first paper of this series, a model for furrow fertigation was presented. The simulation model combined overland water flow (Saint-Venant equations), solute transport (advection-dispersion), and infiltration. Particular attention was paid to the treatment of junctions present in level furrow systems. In this paper, the proposed model is validated using five furrow fertigation evaluations differing in irrigation discharge, fertilizer application timing, and furrow geometry. Model parameters for infiltration and roughness were estimated using error minimization techniques. The error norm was based on observed and simulated values of advance time, flow depth, and fertilizer concentration. Model parameters could be adequately predicted from just one discharge experiment, although the use of more experiments resulted in decreased error. The validated model was applied to the simulation of a level furrow system from the literature. The model adequately reproduced irrigation advance and flow depth. Fertigation events differing in application timing were simulated to identify conditions leading to adequate fertilizer uniformity.},keywords = {},} - A. Serrano-Pacheco, J. Murillo, and P. Garcia-Navarro, "A finite volume method for the simulation of the waves generated by landslides," Journal of hydrology, vol. 373, iss. 3-4, pp. 273-289, 2009.
[Bibtex]@article{Serrano-Pacheco_2009,title = {A finite volume method for the simulation of the waves generated by landslides},author = {Serrano-Pacheco, A. and Murillo, J. and Garcia-Navarro, P.},journal = {JOURNAL OF HYDROLOGY},volume = {373},number = {3-4},pages = {273-289},year = {2009},doi = {10.1016/j.jhydrol.2009.05.003},abstract = {This work deals with the numerical simulation of the surface waves generated by external actions such as landslides. The underlying mathematical model for the unsteady flow is the shallow water system A. finite volume method for the solution of the shallow water system in presence of irregular topography of changing shape is presented. The model and the numerical method are applied to a series of test cases with laboratory data and also to a practical case of realistic size. The numerical model is designed to work on both structured quadrilateral and Unstructured triangular grids and is able to cope with unsteady wetting/drying fronts.},keywords = {},} - J. Murillo, P. Garcia-Navarro, and J. Burguete, "Time step restrictions for well-balanced shallow water solutions in non-zero velocity steady states," International journal for numerical methods in fluids, vol. 60, iss. 12, pp. 1351-1377, 2009.
[Bibtex]@article{Murillo_2009,title = {Time step restrictions for well-balanced shallow water solutions in non-zero velocity steady states},author = {Murillo, J. and Garcia-Navarro, P. and Burguete, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {60},number = {12},pages = {1351-1377},year = {2009},doi = {10.1002/fld.1939},abstract = {Numerical models based on the conservative formulation of the shallow water equations in finite volumes have recently paid special attention to the convenience of a unified discretization of bed slope source terms and pressure momentum fluxes in order to ensure a correct representation of both in steady states. In cases of steady shallow water flow with non-zero velocity, the discrete balance must include the friction term and the good equilibrium of the discrete solution must be revisited. Besides, there is the question of stability. The presence of relatively large friction terms reduces considerably the stability region of the explicit schemes (with either separate or unified discretization). Implicit formulations strongly help to relax the friction related stability restrictions but are only feasible in the context of separated discretization. Therefore, a strategy to blend both approaches (unified explicit and separated implicit) is presented that ensures both a perfect balance in steady state and numerical stability in unsteady cases in the presence of friction terms.},keywords = {},}
2008
- J. Murillo, P. GarcÃa-Navarro, P. Brufau, and J. Burguete, "2D modelling of erosion/deposition processes with suspended load using," Journal of hydraulic research, vol. 46, iss. 1, pp. 99-112, 2008.
[Bibtex]@article{doi:10.1080/00221686.2008.9521847,author = { J. Murillo and P. GarcÃa-Navarro and P. Brufau and J. Burguete },title = {2{D} modelling of erosion/deposition processes with suspended load using},journal = {Journal of Hydraulic Research},volume = {46},number = {1},pages = {99-112},year = {2008},doi = {10.1080/00221686.2008.9521847},URL = {http://www.tandfonline.com/doi/abs/10.1080/00221686.2008.9521847},eprint = {http://www.tandfonline.com/doi/pdf/10.1080/00221686.2008.9521847},abstract = { This work describes a finite volume model applied to solve the coupled shallow water/load transport equations, where low concentrations of sediment load are assumed so that the concentration of the solid fraction is assumed not to influence the equations governing the dynamics. The unsteady simulation of erodible bed requires special attention in the discretization of the bed and friction source terms as important instabilities can arise in some situations. The upwind discretization of the time variable bed slope source terms is presented to provide an exact balance of the numerical fluxes and to guarantee steady-state solutions contrary to the pointwise formulation that leads to instabilities destroying the computation. Robust numerical schemes are presented for both moving and fixed boundaries. In the last case a numerical technique is provided to keep the concentration load bounded for values of CFL (Courant–Friedrichs–Lewy) greater than one and therefore decreasing the necessary computational cost. }} - J. Murillo, P. Garcia-Navarro, and J. Burguete, "Analysis of a second-order upwind method for the simulation of solute transport in 2D shallow water flow," International journal for numerical methods in fluids, vol. 56, iss. 6, pp. 661-686, 2008.
[Bibtex]@article{Murillo_2008,title = {Analysis of a second-order upwind method for the simulation of solute transport in 2{D} shallow water flow},author = {Murillo, J. and Garcia-Navarro, P. and Burguete, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {56},number = {6},pages = {661-686},year = {2008},doi = {10.1002/fld.1546},abstract = {A two-dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first-order upwind technique, a second order in space and time and an extended first-order method are applied to solve the non-diffusive terms in both the flow and solute equations and a centred implicit discretization is applied to the diffusion terms. The stability constraints are studied and the form to avoid oscillatory results in the solute concentration in the presence of complex flow situations is detailed. Some comparisons are carried out in order to show the performance in terms of accuracy of the different options.},keywords = {},} - J. Murillo, P. Garcia-Navarro, P. Brufau, and J. Burguete, "2D modelling of erosion/deposition processes with suspended load using upwind finite volumes," Journal of hydraulic research, vol. 46, iss. 1, pp. 99-112, 2008.
[Bibtex]@article{Murillo_2008,title = {2{D} modelling of erosion/deposition processes with suspended load using upwind finite volumes},author = {Murillo, J. and Garcia-Navarro, P. and Brufau, P. and Burguete, J.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {46},number = {1},pages = {99-112},year = {2008},doi = {},abstract = {This work describes a finite volume model applied to solve the coupled shallow water/load transport equations, where low concentrations of sediment load are assumed so that the concentration of the solid fraction is assumed not to influence the equations governing the dynamics. The unsteady simulation of erodible bed requires special attention in the discretization of the bed and friction source terms as important instabilities can arise in some situations. The upwind discretization of the time variable bed slope source terms is presented to provide an exact balance of the numerical fluxes and to guarantee steady-state solutions contrary to the pointwise formulation that leads to instabilities destroying the computation. Robust numerical schemes are presented for both moving and fixed boundaries. In the last case a numerical technique is provided to keep the concentration load bounded for values of CFL (Courant-Friedrichs-Lewy) greater than one and therefore decreasing the necessary computational cost.},keywords = {},} - J. Burguete, P. Garcia-Navarro, and J. Murillo, "Preserving bounded and conservative solutions of transport in one-dimensional shallow-water flow with upwind numerical schemes: application to fertigation and solute transport in rivers," International journal for numerical methods in fluids, vol. 56, iss. 9, pp. 1731-1764, 2008.
[Bibtex]@article{Burguete_2008,title = {Preserving bounded and conservative solutions of transport in one-dimensional shallow-water flow with upwind numerical schemes: Application to fertigation and solute transport in rivers},author = {Burguete, J. and Garcia-Navarro, P. and Murillo, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {56},number = {9},pages = {1731-1764},year = {2008},doi = {10.1002/fld.1576},abstract = {This work intends to show that conservative upwind schemes based on a separate discretization of the scalar solute transport from the shallow-water equations are unable to preserve uniform solute profiles in situations of one-dimensional unsteady subcritical flow. However, the coupled discretization of the system is proved to lead to the correct solution in first-order approximations. This work is also devoted to show that, when using a coupled discretization, a careful definition of the flux limiter function in second-order TVD schemes is required in order to preserve uniform solute profiles. The work shows that, in cases of subcritical irregular flow, the coupled discretization is necessary but nevertheless not sufficient to ensure concentration distributions free from oscillations and a method to avoid these oscillations is proposed. Examples of steady and unsteady flows in test cases, river and irrigation are presented.},keywords = {},} - E. Playan, O. Perez-Coveta, A. Martinez-Cob, J. Herrero, P. Garcia-Navarro, B. Latorre, P. Brufau, and J. Garces, "Overland water and salt flows in a set of rice paddies," Agricultural water management, vol. 95, iss. 6, pp. 645-658, 2008.
[Bibtex]@article{Playan_2008,title = {Overland water and salt flows in a set of rice paddies},author = {Playan, E. and Perez-Coveta, O. and Martinez-Cob, A. and Herrero, J. and Garcia-Navarro, P. and Latorre, B. and Brufau, P. and Garces, J.},journal = {AGRICULTURAL WATER MANAGEMENT},volume = {95},number = {6},pages = {645-658},year = {2008},doi = {10.1016/j.agwat.2008.01.012},abstract = {Cultivation of paddy rice in semiarid areas of the world faces problems related to water scarcity. This paper aims at characterizing water use in a set of paddies located in the central Ebro basin of Spain using experimentation and computer simulation. A commercial field with six interconnected paddies, with a total area of 5.31 ha, was instrumented to measure discharge and water quality at the inflow and at the runoff outlet. The soil was classified as a Typic Calcixerept, and was characterized by a mild salinity (2.5 dS m(-1)) and an infiltration rate of 5.8 mm day(-1). The evolution of flow depth at all paddies was recorded. Data from the 2002 rice-growing season was elaborated using a mass balance approach to estimate the infiltration rate and the evolution of discharge between paddies. Seasonal crop evapotranspiration, estimated with the surface renewal method, was 731 mm (5.1 mm day(-1)), very similar to that of other summer cereals grown in the area, like corn. The irrigation input was 1874 mm, deep percolation was 830 mm and surface runoff was 372 mm. Irrigation efficiency was estimated as 41%. The quality of surface runoff water was slightly degraded due to evapoconcentration and to the contact with the soil. During the period 2001-2003, the electrical conductivity of surface runoff water was 54% higher than that of irrigation water. However, the runoff water was suitable for irrigation. A mechanistic mass balance model of inter-paddy water flow permitted to conclude that improvements in irrigation efficiency cannot be easily obtained in the experimental conditions. Since deep percolation losses more than double surface runoff losses, a reduction in irrigation discharge would not have much room for efficiency improvement. Simulations also showed that rice irrigation performance was not negatively affected by the fluctuating inflow hydrograph. These hydrographs are typical of turnouts located at the tail end of tertiary irrigation ditches. In fact, these are the sites where rice has been historically cultivated in the study area, since local soils are often saline-sodic and can only grow paddy rice taking advantage of the low salinity of the irrigation water. The low infiltration rate characteristic of these saline-sodic soils (an experimental value of 3.2 mm day(-1) was obtained) combined with a reduced irrigation discharge resulted in a simulated irrigation efficiency of 60%. Paddy rice irrigation efficiency can attain reasonable values in the local saline-sodic soils, where the infiltration rate is clearly smaller than the average daily rice evapotranspiration.},keywords = {},} - J. Burguete, P. Garcia-Navarro, and J. Murillo, "Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: application to unsteady irrigation and river flow," International journal for numerical methods in fluids, vol. 58, iss. 4, pp. 403-425, 2008.
[Bibtex]@article{Burguete_2008,title = {Friction term discretization and limitation to preserve stability and conservation in the 1{D} shallow-water model: Application to unsteady irrigation and river flow},author = {Burguete, J. and Garcia-Navarro, P. and Murillo, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {58},number = {4},pages = {403-425},year = {2008},doi = {10.1002/fld.1727},abstract = {Friction is one of the relevant forces included in the momentum equation of the ID shallow-water model. This work shows that a pointwise discretization of the friction term unbalances this term with the rest of the terms in the equation in steady state. On the other hand, an upwind discretization of the friction term ensures the correct discrete balance. Furthermore, a conservative technique based on the limitation of the friction value is proposed in order to avoid unbounded values of the friction term in unsteady case:; of advancing front over dry and rough surfaces. This limitation improves the quality of unsteady solutions in wet/dry fronts and guarantees the numerical stability in cases with dominant friction terms. The proposed discretization is validated in some test cases with analytical solution or with measured data and used in some practical cases.},keywords = {},}
2007
- J. Burguete, G. P., J. Murillo, and I. Garcia-Palacin, "Analysis of the friction term in the one-dimensional shallow-water model," Journal of hydraulic engineering-asce, vol. 133, iss. 9, pp. 1048-1063, 2007.
[Bibtex]@article{Burguete_2007,title = {Analysis of the friction term in the one-dimensional shallow-water model},author = {Burguete, J. and Garcia-Navarro P. and Murillo, J. and Garcia-Palacin, I.},journal = {JOURNAL OF HYDRAULIC ENGINEERING-ASCE},volume = {133},number = {9},pages = {1048-1063},year = {2007},doi = {10.1061/(ASCE)0733-9429(2007)133:9(1048)},abstract = {The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.},keywords = {},} - J. Murillo, P. Garcia-Navarro, J. Burguete, and P. Brufau, "The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes," International journal for numerical methods in fluids, vol. 54, iss. 5, pp. 543-590, 2007.
[Bibtex]@article{Murillo_2007,title = {The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes},author = {Murillo, J. and Garcia-Navarro, P. and Burguete, J. and Brufau, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {54},number = {5},pages = {543-590},year = {2007},doi = {10.1002/fld.1417},abstract = {The two-dimensional shallow water model is a hyperbolic system of equations considered well suited to simulate unsteady phenomena related to some surface wave propagation. The development of numerical schemes to correctly solve that system of equations finds naturally an initial step in two-dimensional scalar equation, homogeneous or with source terms. We shall first provide a complete formulation of the second-order finite volume scheme for this equation, paying special attention to the reduction of the method to first order as a particular case. The explicit first and second order in space upwind finite volume schemes are analysed to provide an understanding of the stability constraints, making emphasis in the numerical conservation and in the preservation of the positivity property of the solution when necessary in the presence of source terms. The time step requirements for stability are defined at the cell edges, related with the traditional Courant-Friedrichs-Lewy (CFL) condition.},keywords = {},} - E. Toro and P. Garcia-Navarro, "Godunov-type methods for free-surface shallow flows: a review," Journal of hydraulic research, vol. 45, iss. 6, pp. 736-751, 2007.
[Bibtex]@article{Toro_2007,title = {Godunov-type methods for free-surface shallow flows: A review},author = {Toro, EF. and Garcia-Navarro, P.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {45},number = {6},pages = {736-751},year = {2007},doi = {},abstract = {This review paper concerns the application of numerical methods of the Godunov type to the computation of approximate solutions to free-surface gravity flows modelled under a shallow-water type assumption. In the absence of dissipative processes the resulting governing equations are, with rare exceptions, of hyperbolic type. This mathematical property has, in the main, been responsible for the transfer of the Godunov-type numerical methodology, initially developed for the compressible Euler equations of gas dynamics in the aerospace community, to hydraulics and related areas of application. Godunov methods offer distinctive advantages over other methods. For example, they give correct representation of discontinuous waves (bores); this means the correct propagation speed (the methods are conservative), sharp definition of transitions and absence of unphysical oscillations in the vicinity of the wave. Future trends include (i) the use of these methods to deal with physically more complete models without the shallow water assumption and (ii) implementation of very-high order versions of these methods.},keywords = {},}
2006
- J. Burguete, P. Garcia-Navarro, and J. Murillo, "Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flow," International journal for numerical methods in fluids, vol. 51, iss. 6, pp. 585-615, 2006.
[Bibtex]@article{Burguete_2006,title = {Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flow},author = {Burguete, J. and Garcia-Navarro, P. and Murillo, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {51},number = {6},pages = {585-615},year = {2006},doi = {10.1002/fld.1127},abstract = {A revision of some well-known discretization techniques for the numerical boundary conditions in I D shallow-water flow models is presented. More recent options are also considered in the search for a fully conservative technique that is able to preserve the good properties of a conservative scheme used for the interior points. Two conservative numerical schemes are used as representatives of the families of explicit and implicit numerical methods. The implementation of the different boundary options to these schemes is compared by means of the simulation of several test cases with exact solution. The schemes with the global conservation boundary discretization are applied to the simulation of a real river flood wave leading to very satisfactory results.},keywords = {},} - J. Murillo, P. Garcia-Navarro, P. Brufau, and J. Burguete, "Extension of an explicit finite volume method to large time steps (CFL > 1): application to shallow water flows," International journal for numerical methods in fluids, vol. 50, iss. 1, pp. 63-102, 2006.
[Bibtex]@article{Murillo_2006,title = {Extension of an explicit finite volume method to large time steps ({CFL} > 1): application to shallow water flows},author = {Murillo, J. and Garcia-Navarro, P. and Brufau, P. and Burguete, J.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {50},number = {1},pages = {63-102},year = {2006},doi = {10.1002/fld.1036},abstract = {In this work, the explicit First order upwind scheme is presented under a formalism that enables the extension of the methodology to large time steps. The number of cells in the stencil of the numerical scheme is related to the allowable size of the CFL number for numerical stability. It is shown how to increase both at the same time. The basic idea is proposed for a ID scalar equation and extended to ID and 2D non-linear systems with source terms. The importance of the kind of grid used is highlighted and the method is outlined for irregular grids. The good quality of the results is illustrated by means of several examples including shallow water flow test cases. The bed slope source terms are involved in the method through an upwind discretization.},keywords = {},} - J. Murillo, P. Garcia-Navarro, J. Burguete, and P. Brufau, "A conservative 2D model of inundation flow with solute transport over dry bed," International journal for numerical methods in fluids, vol. 52, iss. 10, pp. 1059-1092, 2006.
[Bibtex]@article{Murillo_2006,title = {A conservative 2{D} model of inundation flow with solute transport over dry bed},author = {Murillo, J. and Garcia-Navarro, P. and Burguete, J. and Brufau, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {52},number = {10},pages = {1059-1092},year = {2006},doi = {10.1002/fld.1216},abstract = {In this paper, a transient 2{D} coupled vertically averaged flow/transport model is presented. The model deals with all kind of bed geometries and guarantees global conservation and positive values of both water level and solute concentration in the transient solution. The model is based on an upwind finite volume method, using Roe's approximate Riemann solver. A specific modification of the Riemann solver is proposed to overcome the generation of negative values of depth and concentration, that can appear as a consequence of existing wetting/drying and solute advance fronts over variable bed levels, or by the generation of new ones when dry areas appear. The numerical stability constraints of the explicit model are stated incorporating the influence of the flow velocity, the bed variations and the possible appearance of dry cells. Faced to the important restriction that this new stability condition can impose on the time step size, a different strategy to allow stability using a maximum time step, and in consequence a minimum computational cost is presented.},keywords = {},} - G. Perez, P. Garcia-Navarro, and M. Vazquez-Cendon, "One-dimensional model of shallow water surface waves generated by landslides," Journal of hydraulic engineering-asce, vol. 132, iss. 5, pp. 462-473, 2006.
[Bibtex]@article{Perez_2006,title = {One-dimensional model of shallow water surface waves generated by landslides},author = {Perez, G. and Garcia-Navarro, P. and Vazquez-Cendon, ME.},journal = {JOURNAL OF HYDRAULIC ENGINEERING-ASCE},volume = {132},number = {5},pages = {462-473},year = {2006},doi = {10.1061/(ASCE)07333-9429(2006)132:5(462)},abstract = {A numerical model is presented as the basis for the study of surface waves generated by bank and bottom landslides in rivers. The flow is assumed to be properly modeled by the shallow water equations. The solid movement is introduced in the model as an external action, and assumed rigid and impervious. Two situations are identified in the flow subsequent to a solid movement: longitudinal and transversal sliding. A discussion on the modeling difficulties associated with the latter is included. The flow equations are solved by means of an upwind scheme specially adapted to advancing fronts over dry irregular beds.},keywords = {},}
2005
- J. Murillo, J. Burguete, P. Brufau, and P. Garcia-Navarro, "Coupling between shallow water and solute flow equations: analysis and management of source terms in 2d," International journal for numerical methods in fluids, vol. 49, iss. 3, pp. 267-299, 2005.
[Bibtex]@article{Murillo_2005,title = {Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D},author = {Murillo, J. and Burguete, J. and Brufau, P. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {49},number = {3},pages = {267-299},year = {2005},doi = {10.1002/fld.992},abstract = {A two-dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first order upwind technique is applied to solve the flux terms in both the flow and solute equations and the bed slope source terms and a centred discretization is applied to the diffusion and friction terms. The convenience of considering the fully coupled system of equations is indicated and the methodology is well explained. Three options are suggested and compared in order to deal with the diffusion terms. Some comparisons are carried out in order to show the performance in terms of accuracy and computational effort of the different options.},keywords = {},}
2004
- P. Brufau, P. Garcia-Navarro, and M. Vazquez-Cendon, "Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography," International journal for numerical methods in fluids, vol. 45, iss. 10, pp. 1047-1082, 2004.
[Bibtex]@article{Brufau_2004,title = {Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography},author = {Brufau, P. and Garcia-Navarro, P. and Vazquez-Cendon, ME.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {45},number = {10},pages = {1047-1082},year = {2004},doi = {10.1002/fld.729},abstract = {A wetting-drying condition (WDC) for unsteady shallow water flow in two dimensions leading to zero numerical error in mass conservation is presented in this work. Some applications are shown which demonstrate the effectiveness of the WDC in flood propagation and dam break flows over real geometries. The WDC has been incorporated into a cell centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured meshes. Previous wetting-drying condition based on steady-state conditions lead to numerical errors in unsteady cases over configurations with strong variations on bed slope. A modification of the wetting-drying condition including the normal velocity to the cell edge enables to achieve zero numerical errors. The complete numerical technique is described in this work including source terms discretization as a complete and efficient 2D river flow simulation tool. Comparisons of experimental and numerical results are shown for some of the applications.},keywords = {},} - J. Burguete and P. Garcia-Navarro, "Improving simple explicit methods for unsteady open channel and river flow," International journal for numerical methods in fluids, vol. 45, iss. 2, pp. 125-156, 2004.
[Bibtex]@article{Burguete_2004,title = {Improving simple explicit methods for unsteady open channel and river flow},author = {Burguete, J. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {45},number = {2},pages = {125-156},year = {2004},doi = {10.1002/fld.619},abstract = {av3 A rigorous study of the explicit Lax-Friedrichs scheme for its application to one-dimensional shallow water flows is presented. The deficiencies of this method are identified and the way to overcome them are presented. It is compared to the explicit first order upwind scheme and to the explicit second order Lax-Wendroff scheme by means of the simulation of several test cases with exact solution. All three schemes in their best balanced version are applied to the simulation of a real river flood wave leading to very satisfactory results.},keywords = {},} - J. Burguete and P. Garcia-Navarro, "Implicit schemes with large time step for non-linear equations: application to river flow hydraulics," International journal for numerical methods in fluids, vol. 46, iss. 6, pp. 607-636, 2004.
[Bibtex]@article{Burguete_2004,title = {Implicit schemes with large time step for non-linear equations: application to river flow hydraulics},author = {Burguete, J. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {46},number = {6},pages = {607-636},year = {2004},doi = {10.1002/fld.772},abstract = {In this work, first-order upwind implicit schemes are considered. The traditional tridiagonal scheme is rewritten as a SLIM of two bidiagonal schemes in order to produce a simpler method better suited for unsteady transcritical flows. On the other hand, the origin of the instabilities associated to the use of upwind implicit methods for shock propagations is identified and a new stability condition for non-linear problems is proposed. This modification produces a robust, simple and accurate upwind semi-explicit scheme suitable for discontinuous flows with high Courant-Friedrichs-Lewy (CFL) numbers. The discretization at the boundaries is based on the condition of global mass conservation thus enabling a fully conservative solution for all kind of boundary conditions. The performance of the proposed technique will be shown in the solution of the inviscid Burgers' equation, in an ideal dambreak test case, in some steady open channel flow test cases with analytical solution and in a realistic flood routing problem, where stable and accurate solutions will be presented using CFL values up to 100.},keywords = {},} - P. Garcia-Navarro, A. Sanchez, N. Clavero, and E. Playan, "Simulation model for level furrows. ii: description, validation, and application," Journal of irrigation and drainage engineering-asce, vol. 130, iss. 2, pp. 113-121, 2004.
[Bibtex]@article{Garcia-Navarro_2004,title = {Simulation model for level furrows. II: Description, validation, and application},author = {Garcia-Navarro, P. and Sanchez, A. and Clavero, N. and Playan, E.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {130},number = {2},pages = {113-121},year = {2004},doi = {10.1061/(ASCE)0733-9437(2004)130:2(113)},abstract = {In a companion paper, experimental evidence was elaborated to confirm that in particular circumstances the performance of level-furrow irrigation can exceed that of level-basin irrigation. The application of a single furrow simulation model to an irrigation event in a level-furrow field resulted in large estimation errors. To overcome them, the development and validation of a numerical model of level-furrow irrigation is reported in this work. The model is based on the interconnection of a number of one-dimensional channels. The individual channels are connected using confluence or bifurcation points. Furrow infiltration is modelled through a Kostiakov infiltration equation including the furrow discharge as an independent variable. The proposed model is validated using the experimental level furrow evaluation presented in the companion paper. Finally, the model is applied to explore the conditions in which level furrow irrigation can outperform level basin irrigation. The proposed model stands as a valuable tool in the design and management of level furrow irrigation systems.},keywords = {},} - E. Playan, J. Rodriguez, and P. Garcia-Navarro, "Simulation model for level furrows. i: analysis of field experiments," Journal of irrigation and drainage engineering-asce, vol. 130, iss. 2, pp. 106-112, 2004.
[Bibtex]@article{Playan_2004,title = {Simulation model for level furrows. I: Analysis of field experiments},author = {Playan, E. and Rodriguez, JA. and Garcia-Navarro, P.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {130},number = {2},pages = {106-112},year = {2004},doi = {10.1061/(ASCE)0733-9437(2004)130:2(106)},abstract = {The level-furrow irrigation system consists of furrowing a level basin. In level furrows, irrigation proceeds just like in level basins: the field is flooded from one point and water spreads to irrigate each furrow. Several writers have reported that this irrigation system has the potential to conserve water as compared to level-basin irrigation. However, no comparative studies on the performance of both irrigation systems are available, and the simulation of level furrows has not been attempted. In this work, two field experiments are reported. Both of them were performed in the same soil and in the same conditions. In the first experiment, infiltration was estimated for a series of furrow irrigation discharges and for a level basin. In the second experiment, a level furrow irrigation event was evaluated. A simulated level basin irrigation event in the level furrow experimental field required six times more time and water to complete advance. Infiltration equations including the irrigation discharge or the wetted perimeter as independent variables were proposed for the experimental furrow conditions. Application of a furrow simulation model to the level-furrow experiment resulted in an underestimation of the time of advance. To overcome this problem, a simulation model for level furrows was developed and is presented in a companion paper. The reported field experiments were used to validate the model, which was applied (in a companion paper) to explore adequate conditions for level furrow irrigation performance.},keywords = {},}
2003
- P. Brufau and P. Garcia-Navarro, "Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique," Journal of computational physics, vol. 186, iss. 2, pp. 503-526, 2003.
[Bibtex]@article{Brufau_2003,title = {Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique},author = {Brufau, P. and Garcia-Navarro, P.},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {186},number = {2},pages = {503-526},year = {2003},doi = {10.1016/S0021-9991(03)00072-X},abstract = {In the context of numerical techniques for solving unsteady free surface problems, finite element and finite volume approximations are widely used. A class of upwind methods which attempts to model the equations in a genuinely multidimensional manner has been recently introduced as an alternative. Multidimensional upwind schemes (MUS) were developed initially for the approximation of steady-state solutions of the two-dimensional Euler equations on unstructured grids, although they can be applicable to any system of hyperbolic conservation laws, such as the shallow water equations. The formal analogy between the two systems of equations is useful for simple cases. However, in practical applications of interest in hydraulics, complex geometries and bottom slope variation can lead to important numerical errors produced by an inadequate source term discretization. This problem has been analyzed and, in this work, the necessity of a multidimensional upwind discretization of the source terms is justified. The basis of the numerical method is stated and the particular adaptation to unsteady shallow water flows over irregular geometry is described. As test cases, laboratory experimental data are used together with academic tests for validation.},keywords = {},} - P. Garcia-Navarro, P. Brufau, J. Murillo, and C. Zorraquino, "Estudio hidraulico del riesgo de inundacion en el meandro de ranillas: modelos de simulacion numerica," Ingenieria del agua, vol. 10, pp. 115-125, 2003.
[Bibtex]@article{Murillo_2009,title = {Estudio hidraulico del riesgo de inundacion en el meandro de Ranillas: Modelos de simulacion numerica},author = {Garcia-Navarro, P. and Brufau, P. and Murillo, J. and Zorraquino, C.},journal = {Ingenieria del Agua},volume = {10},pages = {115-125},year = {2003},}
2002
- P. E. Brufau P. Garcia-Navarro P. and N. Zapata, "Numerical modeling of basin irrigation with an upwind scheme," Journal of irrigation and drainage engineering-asce, vol. 128, iss. 4, pp. 212-223, 2002.
[Bibtex]@article{Brufau_2002,title = {Numerical modeling of basin irrigation with an upwind scheme},author = {Brufau P., Garcia-Navarro P., Playan E. and Zapata, N.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {128},number = {4},pages = {212-223},year = {2002},doi = {10.1061/(ASCE)0733-9437(2002)128:4(212)},abstract = {In recent years, upwind techniques have been successfully applied in hydrology to simulate two-dimensional free surface flows. Basin irrigation is a surface irrigation system characterized by its potential to use water very efficiently. In basin irrigation, the field is leveled to zero slope and flooded from a point source. The quality of land leveling has been shown to influence irrigation performance drastically. Recently, two-dimensional numerical models have been developed as tools to design and manage basin irrigation systems. In this work, a finite volume-based upwind scheme is used to build a simulation model considering differences in bottom level. The discretization is made on triangular or quadrilateral unstructured grids and the source terms of the equations are given a special treatment. The model is applied to the simulation of two field experiments. Simulation results resulted in a clear improvement over previous simulation efforts and in a close agreement with experimental data. The proposed model has proved its ability to simulate overland flow in the presence of undulated bottom elevations, inflow hydrographs, and colliding fronts.},keywords = {},} - P. Brufau, M. Vazquez-Cendon, and P. Garcia-Navarro, "A numerical model for the flooding and drying of irregular domains," International journal for numerical methods in fluids, vol. 39, iss. 3, pp. 247-275, 2002.
[Bibtex]@article{Brufau_2002,title = {A numerical model for the flooding and drying of irregular domains},author = {Brufau, P. and Vazquez-Cendon, ME. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {39},number = {3},pages = {247-275},year = {2002},doi = {10.1002/fld.285},abstract = {A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell-centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests.},keywords = {},} - A. Sanchez, P. Garcia-Navarro, and E. Playan, "Modelo de simulacion de riego por surcos inundados," Ingenieria del agua, vol. 9, pp. 333-343, 2002.
[Bibtex]@article{Murillo_2009,title = {Modelo de simulacion de riego por surcos inundados},author = {Sanchez, A. and Garcia-Navarro, P. and Playan, E.},journal = {Ingenieria del Agua},volume = {9},pages = {333-343},year = {2002},}
2001
- J. Burguete and P. Garcia-Navarro, "Efficient construction of high-resolution tvd conservative schemes for equations with source terms: application to shallow water flows," International journal for numerical methods in fluids, vol. 37, iss. 2, pp. 209-248, 2001.
[Bibtex]@article{Burguete_2001,title = {Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows},author = {Burguete, J. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {37},number = {2},pages = {209-248},year = {2001},doi = {},abstract = {High-resolution total variation diminishing (TVD) schemes are widely used for the numerical approximation of hyperbolic conservation laws. Their extension to equations with source terms involving spatial derivatives is not obvious. In this work, efficient ways of constructing conservative schemes from the conservative, non-conservative or characteristic form of the equations are described in detail. An upwind, as opposed to a pointwise, treatment of the source terms is adopted here, and a new technique is proposed in which source terms are included in the flux limiter functions to get a complete second-order compact scheme. A new correction to fix the entropy problem is also presented and a robust treatment of the boundary conditions according to the discretization used is stated.},keywords = {},} - M. Castro and P. Garcia-Navarro, "The application of a conservative grid adaptation technique to 1D shallow water equations," Mathematical and computer modelling, vol. 34, iss. 1-2, pp. 29-35, 2001.
[Bibtex]@article{Castro_2001,title = {The application of a conservative grid adaptation technique to 1{D} shallow water equations},author = {Castro, MJ. and Garcia-Navarro, P.},journal = {MATHEMATICAL AND COMPUTER MODELLING},volume = {34},number = {1-2},pages = {29-35},year = {2001},doi = {},abstract = {In this contribution, we present an efficient conservative mesh adaptation algorithm applied to 1D shallow water equations. This algorithm is suitable for unsteady situations and discontinuities of the solutions are well captured. Numerical results are presented.},keywords = {},} - P. Brufau and P. Garcia-Navarro, "Modelo de simulacion bidimensional de transitorios en aguas superficiales: aplicacion a roturas de presa," Ingenieria civil, vol. 121, pp. 33-40, 2001.
[Bibtex]@article{Murillo_2009,title = {Modelo de simulacion bidimensional de transitorios en aguas superficiales: aplicacion a roturas de presa},author = {Brufau, P. and Garcia-Navarro, P.},journal = {Ingenieria Civil},volume = {121},pages = {33-40},year = {2001},}
2000
- P. Brufau and P. Garcia-Navarro, "Two-dimensional dam break flow simulation," International journal for numerical methods in fluids, vol. 33, iss. 1, pp. 35-57, 2000.
[Bibtex]@article{Brufau_2000,title = {Two-dimensional dam break flow simulation},author = {Brufau, P. and Garcia-Navarro, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {33},number = {1},pages = {35-57},year = {2000},doi = {},abstract = {Numerical modelling of shallow water flow in two dimensions is presented in this work with the results obtained in dam break tests. Free surface flow in channels can be described mathematically by the shallow-water system of equations. These equations have been discretized using an approach based on unstructured Delaunay triangles and applied to the simulation of two-dimensional dam break flows. A cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first- and second-order accuracy. Special treatment of the friction term has been adopted and will be described. The scheme is capable of handling complex flow domains as shown in the simulation corresponding to the test cases proposed, i.e. that of a dam break wave propagating into a 45 degrees bend channel (UCL) and in a channel with a constriction (LNEC-IST). Comparisons of experimental and numerical results are shown.},keywords = {},} - P. Brufau, P. Garcia-Navarro, G. P., L. Natale, and F. Savi, "1D mathematical modelling of debris flow," Journal of hydraulic research, vol. 38, iss. 6, pp. 435-446, 2000.
[Bibtex]@article{Brufau_2000,title = {1{D} Mathematical modelling of debris flow},author = {Brufau, P. and Garcia-Navarro, P. and Ghilardi P. and Natale, L. and Savi, F.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {38},number = {6},pages = {435-446},year = {2000},doi = {},abstract = {Debris flow is modelled using the equations governing the dynamics of a liquid-solid mixture. An upwind finite volume scheme;is applied to solve the resulting differential equations in one dimension. These equations have a structure similar to those of the monophasic water flow, differing from them by the presence of some terms characteristic of the bifasic nature of the mixture, such as granular bed erosion velocity, sediment concentration bed shear stress, etc. The model and the system of equations to be solved are presented with the description of the implementation of the upwind scheme for the resulting hyperbolic conservation system. The numerical method is first order in both space and time. The treatment of the, source terms is specified in detail and some comparison with laboratory experiments are presented.},keywords = {},} - P. Garcia-Navarro, E. Playan, and N. Zapata, "Solute transport modeling in overland flow applied to fertigation," Journal of irrigation and drainage engineering-asce, vol. 126, iss. 1, pp. 33-40, 2000.
[Bibtex]@article{Garcia-Navarro_2000,title = {Solute transport modeling in overland flow applied to fertigation},author = {Garcia-Navarro, P. and Playan, E. and Zapata, N.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {126},number = {1},pages = {33-40},year = {2000},doi = {},abstract = {A model of solute transport in overland flow is developed and applied to the simulation of surface fertigation. Water flow is simulated using the depth-averaged, 1D shallow water equations. Solute how is represented by an advection-diffusion model. The resulting set of three partial differential equations is sequentially solved at each time step. First, water flow is computed using the explicit two-step McCormack method. Based on the obtained velocity field, solute transport is explicitly determined from the advection-diffusion equation using the operator split technique. Four held experiments involving fertigation events on an impervious free-draining border were performed to validate the proposed model and to obtain estimates of Kx, the longitudinal dispersion coefficient. A value of Kx = 0.075 m(2) s(-1) satisfactorily reproduces the field experiments. The model is also applied to the simulation of a fertigation event on a pervious border. A sensitivity analysis is performed to assess the dependence of fertilizer distribution uniformity on the value of Kx. Finally, the proposed model is compared with a previous model based on pure advection.},keywords = {},} - P. Garcia-Navarro and M. Vazquez-Cendon, "On numerical treatment of the source terms in the shallow water equations," Computers & fluids, vol. 29, iss. 8, pp. 951-979, 2000.
[Bibtex]@article{Garcia-Navarro_2000,title = {On numerical treatment of the source terms in the shallow water equations},author = {Garcia-Navarro, P. and Vazquez-Cendon, ME.},journal = {COMPUTERS & FLUIDS},volume = {29},number = {8},pages = {951-979},year = {2000},doi = {},abstract = {Upwind schemes are very well adapted to advection dominated flows and have become popular for applications involving the Euler system of equations. Recently, Riemann solver-based techniques such as Roe's scheme have become a successful tool for numerical simulation of other conservation laws like the shallow water equations. One of the disadvantages of this technique is related to the treatment of the source terms of the equations. The conservativity of the scheme can be seriously damaged if a careless treatment is applied. Previous papers studied the way to treat the terms arising from bed level changes. This gaper deals with the analysis of the main reasons leading to a correct treatment of the geometrical source terms, that is, those representing the changes in cross-section which may be linked to the specific dependence of the flux function on the geometry.},keywords = {},} - M. Hubbard and P. Garcia-Navarro, "Flux difference splitting and the balancing of source terms and flux gradients," Journal of computational physics, vol. 165, iss. 1, pp. 89-125, 2000.
[Bibtex]@article{Hubbard_2000,title = {Flux difference splitting and the balancing of source terms and flux gradients},author = {Hubbard, ME. and Garcia-Navarro, P.},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {165},number = {1},pages = {89-125},year = {2000},doi = {},abstract = {Flux difference splitting methods are widely used for the numerical approximation of homogeneous conservation laws where the flux depends only on the conservative variables. However, in many practical situations this is not the case. Not only are source terms commonly part of the mathematical model, but also the Aux can vary spatially even when the conservative variables do not. It is the discretisation of the additional terms arising from these two situations which is addressed in this work, given that a specific flux difference splitting method has been used to approximate the underlying conservation law. The discretisation is constructed in a manner which retains an exact balance between the flux gradients and the source terms when this is appropriate. The effectiveness of these new techniques, in both one and two dimensions, is illustrated using the shallow water equations, in which the additional terms arise from the modelling of bed slope and, in one dimension, breadth variation. Roe's scheme is chosen for the approximation of the conservation laws and appropriate discrete forms are constructed for the additional terms, not only in the first-order case but also in the presence of flux- and slope-limited high-resolution corrections. The method is then extended to two-dimensional flow where it can be applied on both quadrilateral and triangular grids.},keywords = {},} - P. Brufau and P. Garcia-Navarro, "Esquemas de alta resolucion para resolver las ecuaciones de shallow water," Revista internacional de metodos numericos para calculo y diseño en ingenieria, vol. 16, pp. 493-512, 2000.
[Bibtex]@article{Murillo_2009,title = {Esquemas de alta resolucion para resolver las ecuaciones de shallow water},author = {Brufau, P. and Garcia-Navarro, P.},journal = {Revista Internacional de Metodos Numericos para Calculo y Diseño en Ingenieria},volume = {16},pages = {493-512},year = {2000},}
1999
- P. Garcia-Navarro, A. Fras, and I. Villanueva, "Dam-break flow simulation: some results for one-dimensional models of real cases," Journal of hydrology, vol. 216, iss. 3-4, pp. 227-247, 1999.
[Bibtex]@article{Garcia-Navarro_1999,title = {Dam-break flow simulation: some results for one-dimensional models of real cases},author = {Garcia-Navarro, P. and Fras, A. and Villanueva, I.},journal = {JOURNAL OF HYDROLOGY},volume = {216},number = {3-4},pages = {227-247},year = {1999},doi = {},abstract = {In many countries, the determination of the parameters of the wave, likely to be produced after the failure of a dam, is required by law, and systematic studies are mandatory. There is a necessity to develop adequate numerical solvers which are able to reproduce situations originated from the irregularities of a non-prismatic bed and to model the complete equations that progress despite the irregular character of the data. Many hydraulic situations can be described by means of a one-dimensional (1D) model, either because a more detailed resolution is unnecessary or because the flow is markedly ID. Many techniques have been developed recently for systems of conservation laws in 1D tin the context of gas dynamics). Some years after their adoption for solving problems in gas dynamics, upwind and total variation diminishing (TVD) numerical schemes have been successfully used for the solution of the shallow water equations, with similar advantages. Their use is nevertheless only gradually gaining acceptance in this sector. The performance of some of these techniques for practical applications in river flow is reported in this work.},keywords = {},} - I. Villanueva, P. Garcia-Navarro, and V. Zorraquino, "Validacion experimental de un modelo computacional unidimensional para el calculo de ondas de avenida," Ingenieria del agua, vol. 6, pp. 55-63, 1999.
[Bibtex]@article{Murillo_2009,title = {Validacion experimental de un modelo computacional unidimensional para el calculo de ondas de avenida},author = {Villanueva, I. and Garcia-Navarro, P. and Zorraquino, V.},journal = {Ingenieria del Agua},volume = {6},pages = {55-63},year = {1999},}
1997
- E. Playan and P. GarciaNavarro, "Radial flow modeling for estimating level-basin irrigation parameters," Journal of irrigation and drainage engineering-asce, vol. 123, iss. 4, pp. 229-237, 1997.
[Bibtex]@article{Playan_1997,title = {Radial flow modeling for estimating level-basin irrigation parameters},author = {Playan, E. and GarciaNavarro, P.},journal = {JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING-ASCE},volume = {123},number = {4},pages = {229-237},year = {1997},doi = {},abstract = {Previous research in the estimation of surface irrigation parameters from advance time or surface profile observations has focused on the development of solutions for parallel surface flow conditions. This study was conducted to assess the usefulness of a polar model simulating radial flow in the estimation of infiltration and roughness parameters of a point-inflow level-basin irrigation event. The two-step explicit McCormack scheme was applied to the solution of the governing equations. The method of characteristics was used at boundary nodes. Point-wise semiimplicit discretization of the friction and geometric source terms was used. Results of this model compared well with those obtained with a two-dimensional Cartesian model simulating radial flow. Gradient and nongradient minimization techniques were applied to determine pairs of infiltration and roughness parameters. The estimation of the parameters is as feasible for radial flow as it is for parallel flow.},keywords = {},}
1995
- M. GARCIA-NAVARRO P.and HUBBARD and A. PRIESTLEY, "Genuinely multidimensional upwinding for the 2D shallow-water equations," Journal of computational physics, vol. 121, iss. 1, pp. 79-93, 1995.
[Bibtex]@article{GARCIANAVARRO_1995,title = {GENUINELY MULTIDIMENSIONAL UPWINDING FOR THE 2{D} SHALLOW-WATER EQUATIONS},author = {GARCIA-NAVARRO, P.and HUBBARD, ME. and PRIESTLEY, A.},journal = {JOURNAL OF COMPUTATIONAL PHYSICS},volume = {121},number = {1},pages = {79-93},year = {1995},doi = {},abstract = {A multidimensional upwinding technique is applied to the simulation of 2D shallow water flows. It is adapted from fluctuation splitting methods recently proposed for the solution of the Euler system of equations on unstructured triangular grids. The basis of the numerical method is stated and the particular adaptation to the shallow water system is described. Numerical results of interest to hydraulic engineers are presented. Despite the complexities, advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use.},keywords = {},} - P. Garcia-Navarro and F. Alcrudo, "Simulacion de flujo transitorio en cauces naturales," Ingenieria del agua, vol. 2, pp. 7-18, 1995.
[Bibtex]@article{Murillo_2009,title = {Simulacion de flujo transitorio en cauces naturales},author = {Garcia-Navarro, P. and Alcrudo, F.},journal = {Ingenieria del Agua},volume = {2},pages = {7-18},year = {1995},}
1994
- P. GARCIA-NAVARRO and A. PRIESTLEY, "A conservative and shape-preserving semi-lagrangian method for the solution of the shallow-water equations," International journal for numerical methods in fluids, vol. 18, iss. 3, pp. 273-294, 1994.
[Bibtex]@article{GARCIANAVARRO_1994,title = {A CONSERVATIVE AND SHAPE-PRESERVING SEMI-LAGRANGIAN METHOD FOR THE SOLUTION OF THE SHALLOW-WATER EQUATIONS},author = {GARCIA-NAVARRO, P. and PRIESTLEY, A.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {18},number = {3},pages = {273-294},year = {1994},doi = {},abstract = {Semi-Lagrangian methods are now perhaps the most widely researched algorithms in connection with atmospheric flow simulation codes. In order to investigate their applicability to hydraulic problems, cubic Hermite polynomials are used as the interpolant technique. The main advantage of such an approach is the use of information from only two points. The derivatives are calculated and limited so as to produce a shape-preserving solution. The lack of conservation of semi-Lagrangian methods, however, is widely regarded as a serious disadvantage for hydraulic studies, where non-linear problems in which shocks may develop are often encountered. In this work we describe how to make the scheme conservative using an FCT approach. The method proposed does not guarantee an unconditional shock-capturing ability but is able to correctly reproduce the discontinuous flows common in open channel simulation without any shock-fitting algorithm. It is a cheap way to improve existing 1D semi-Lagrangian codes and allows stable calculations beyond the usual CFL limits. A basic semi-Lagrangian method is presented that provides excellent results for a linear problem; the new techniques allow us to tackle non-linear cases without unduly degrading the accuracy for the simpler problems. Two one-dimensional hydraulic problems are used as test cases, water hammer and dam break. In the latter case, because of the non-linearity, special care is needed with the low-order solution and we show the advantages of using Leveque's large-time step version of Roe's scheme for this purpose.},keywords = {},} - P. GARCIA-NAVARRO, F. ALCRUDO, and A. PRIESTLEY, "An implicit method for water-flow modeling in channels and pipes," Journal of hydraulic research, vol. 32, iss. 5, pp. 721-742, 1994.
[Bibtex]@article{GARCIANAVARRO_1994,title = {AN IMPLICIT METHOD FOR WATER-FLOW MODELING IN CHANNELS AND PIPES},author = {GARCIA-NAVARRO, P. and ALCRUDO, F. and PRIESTLEY, A.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {32},number = {5},pages = {721-742},year = {1994},doi = {},abstract = {An implicit time integration method for the simulation of steady and unsteady flow in pipes and channels is presented. It is based on the theory of Total Variation Diminishing (TVD) methods. A conservative linearization leads to a block tridiagonal system of equations which can be cheaply solved by means of a non-iterative matrix decomposition method. It keeps the advantages of classical implicit schemes, and properly deals with all kinds of flow. It is specially suited for steady flows including phenomena such as hydraulic jumps and also gives satisfactory results for time dependent problems. Several test cases are shown to illustrate the performance of this implicit technique in single channels and networks.},keywords = {},}
1993
- F. ALCRUDO and P. GARCIA-NAVARRO, "A high-resolution godunov-type scheme in finite volumes for the 2d shallow-water equations," International journal for numerical methods in fluids, vol. 16, iss. 6, pp. 489-505, 1993.
[Bibtex]@article{ALCRUDO_1993,title = {A HIGH-RESOLUTION GODUNOV-TYPE SCHEME IN FINITE VOLUMES FOR THE 2D SHALLOW-WATER EQUATIONS},author = {ALCRUDO, F. and GARCIA-NAVARRO, P.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {16},number = {6},pages = {489-505},year = {1993},doi = {},abstract = {A high-order Godunov-type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2{D} free-surface flow equations. In order to apply a finite volume technique of integration over body-fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries. Verification of the technique is made by comparison with analytical solutions and very good agreement is found. Three cases of rapidly varying two-dimensional flows are presented to show the efficiency and stability of this method, which contains no terms depending on adjustable parameters. It can be considered well suited for computation of rather complex free-surface two-dimensional problems.},keywords = {},} - P. GARCIA-NAVARRO, "Surges through an open channel junction," Journal of hydraulic research, vol. 31, iss. 1, pp. 79-87, 1993.
[Bibtex]@article{GARCIANAVARRO_1993,title = {SURGES THROUGH AN OPEN CHANNEL JUNCTION},author = {GARCIA-NAVARRO, P.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {31},number = {1},pages = {79-87},year = {1993},doi = {},abstract = {This paper is concerned with the study of the unsteady problem associated with numerical simulation of bore propagation through junctions, and the statement of some of its main features from the point of view of a one dimensional approach. In order to ensure the correct treatment of the involved internal boundary problem when trying to include it in a modelling system, compatibility conditions must be applied with care. The usual technique is to assume the equality among the water levels at the junction. It is shown that this is a valid approximation only for a few simplified cases. A theoretical approach is used to state the unsteady compatibility conditions to be used in the development of a one-dimensional simulation model including supercritical flows and shock propagation through the junction. Some numerical results are presented to illustrate the performance of the suggested techniques. The study does not pretend to be a programming guide but a basic discussion and, as a contribution to the evidence for and against the current technics, it becomes useful to improve modelling systems involving tributaries.},keywords = {},} - P. GARCIA-NAVARRO and V. ZORRAQUINO, "Numerical modeling of flood propagation through system of reservoirs," Journal of hydraulic engineering-asce, vol. 119, iss. 3, pp. 380-389, 1993.
[Bibtex]@article{GARCIANAVARRO_1993,title = {NUMERICAL MODELING OF FLOOD PROPAGATION THROUGH SYSTEM OF RESERVOIRS},author = {GARCIA-NAVARRO, P. and ZORRAQUINO, V.},journal = {JOURNAL OF HYDRAULIC ENGINEERING-ASCE},volume = {119},number = {3},pages = {380-389},year = {1993},doi = {},abstract = {An explicit numerical flow-routing model is developed based on the second order McCormack scheme. This paper describes the use of the finite difference scheme for the solution of the St. Venant equations of the one-dimensional unsteady open channel flow, and the treatment of the boundary problem by the method of characteristics. A case study is presented using the system of reservoirs and the fluvial network of tributaries of the left-hand side of the Ebro River valley in Spain. To get an estimate of the regulating action provided by those reservoirs during the strong rainfall of the first days of November 1982, the registered inflow and outflow hydrographs are used for the simulation of the propagation of the waves along the watercourses. Results of flow computations are presented and compared with field measurements to show that this model can be considered a suitable technique for hydraulic studies involving rapidly varying flows.},keywords = {},}
1992
- F. ALCRUDO, P. GARCIA-NAVARRO, and J. SAVIRON, "Flux difference splitting for 1D open channel flow equations," International journal for numerical methods in fluids, vol. 14, iss. 9, pp. 1009-1018, 1992.
[Bibtex]@article{ALCRUDO_1992,title = {FLUX DIFFERENCE SPLITTING FOR 1{D} OPEN CHANNEL FLOW EQUATIONS},author = {ALCRUDO, F. and GARCIA-NAVARRO, P. and SAVIRON, JM.},journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS},volume = {14},number = {9},pages = {1009-1018},year = {1992},doi = {},abstract = {An upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equations. Added limited second-order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.},keywords = {},} - P. GARCIA-NAVARRO and J. SAVIRON, "Mccormack method for the numerical-simulation of one-dimensional discontinuous unsteady open channel flow," Journal of hydraulic research, vol. 30, iss. 1, pp. 95-105, 1992.
[Bibtex]@article{GARCIANAVARRO_1992,title = {MCCORMACK METHOD FOR THE NUMERICAL-SIMULATION OF ONE-DIMENSIONAL DISCONTINUOUS UNSTEADY OPEN CHANNEL FLOW},author = {GARCIA-NAVARRO, P. and SAVIRON, JM.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {30},number = {1},pages = {95-105},year = {1992},doi = {},abstract = {This paper describes the use of the McCormack explicit finite difference scheme and the treatment of the boundary problem in the development of a one-dimensional simulation model that solves the St. Venant equations of the unsteady, open channel flow. External and internal boundaries are considered. Various illustrative cases are presented to show the efficiency of this technique.},keywords = {},} - M. GARCIA-NAVARRO and J. SAVIRON, "Numerical-simulation of unsteady-flow at open channel junctions," Journal of hydraulic research, vol. 30, iss. 5, pp. 595-609, 1992.
[Bibtex]@article{GARCIANAVARRO_1992,title = {NUMERICAL-SIMULATION OF UNSTEADY-FLOW AT OPEN CHANNEL JUNCTIONS},author = {GARCIA-NAVARRO, MP. and SAVIRON, JM.},journal = {JOURNAL OF HYDRAULIC RESEARCH},volume = {30},number = {5},pages = {595-609},year = {1992},doi = {},abstract = {In this work, some considerations about the problem of the unsteady flow simulation at a junction of open channels are presented. When simulating unsteady flow through junctions, the usual technique is to assume the equality of water stages. Following the theory of characteristics, we explain that this is a valid approximation for low Froude numbers but impossible to apply in other general cases. A theoretical approach of the steady state at a junction is used to state the unsteady compatibility conditions to be used. A time evolution modelling including supercritical flows, hydraulics jumps and shock propagation through the junction becomes possible and a useful tool to improve complex dam break simulations involving tributaries.},keywords = {},} - P. GARCIA-NAVARRO, F. ALCRUDO, and J. SAVIRON, "1-d open-channel flow simulation using tvd-mccormack scheme," Journal of hydraulic engineering-asce, vol. 118, iss. 10, pp. 1359-1372, 1992.
[Bibtex]@article{GARCIANAVARRO_1992,title = {1-D OPEN-CHANNEL FLOW SIMULATION USING TVD-MCCORMACK SCHEME},author = {GARCIA-NAVARRO, P. and ALCRUDO, F. and SAVIRON, JM.},journal = {JOURNAL OF HYDRAULIC ENGINEERING-ASCE},volume = {118},number = {10},pages = {1359-1372},year = {1992},doi = {},abstract = {The addition of a dissipation step to the widely used McCormack numerical scheme is proposed for solving one-dimensional open-channel flow equations. The extra step is devised according to the theory of total variation diminishing (TVD) schemes that are capable of capturing sharp discontinuities without generating the spurious oscillations that more classical methods do. At the same time, the extra step does not introduce any additional difficulty for the treatment of the source terms of the equations. Results from several computations arc presented and comparison with the analytical solution for some test problems is shown. The overall performance of the method can be considered verv good, and it allows for accurate open-channel flow computations involving hydraulic jumps and bores.},keywords = {},} - P. Garcia-Navarro and J. Saviron, "Aplicacion del metodo de mccormack para la simulacion del flujo no estacionario discontinuo en canales de superficie libre," Ingenieria civil, vol. 82, pp. 139-145, 1992.
[Bibtex]@article{Murillo_2009,title = {Aplicacion del metodo de McCormack para la simulacion del flujo no estacionario discontinuo en canales de superficie libre},author = {Garcia-Navarro, P. and Saviron, JM.},journal = {Ingenieria Civil},volume = {82},pages = {139-145},year = {1992},} - P. Garcia-Navarro and J. Saviron, "Simulacion numerica del flujo no estacionario en las confluencias de canales. condiciones de contorno," Ingenieria civil, vol. 82, pp. 145-153, 1992.
[Bibtex]@article{Murillo_2009,title = {Simulacion numerica del flujo no estacionario en las confluencias de canales. Condiciones de contorno},author = {Garcia-Navarro, P. and Saviron, JM.},journal = {Ingenieria Civil},volume = {82},pages = {145-153},year = {1992},}
- J. L. Gracia, A. Navas-Montilla, and E. O'Riordan, "Parameter-uniform numerical methods for singularly perturbed linear transport problems," Mathematical methods in the applied sciences, vol. 45, iss. 17} YEAR = {2022, pp. 11224-11245.
[Bibtex]@Article{adrian02,AUTHOR = {Gracia, J.L. and Navas-Montilla, A. and O'Riordan, E.},TITLE = {Parameter-uniform numerical methods for singularly perturbed linear transport problems},JOURNAL = {Mathematical Methods in the Applied Sciences},VOLUME = {45},NUMBER = {17}YEAR = {2022},PAGES = {11224-11245},}