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Solving shallow-water systems in 2D domains using Finite Volume methods and multimedia SSE instructions
M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida and C. Parés Journal of Computational and Applied Mathematics 221(1) 16 (2008) https://doi.org/10.1016/j.cam.2007.10.034
A Roe-type scheme for two-phase shallow granular flows over variable topography
Marica Pelanti, François Bouchut and Anne Mangeney ESAIM: Mathematical Modelling and Numerical Analysis 42(5) 851 (2008) https://doi.org/10.1051/m2an:2008029
Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes
Manuel J. Castro, Philippe G. LeFloch, María Luz Muñoz-Ruiz and Carlos Parés Journal of Computational Physics 227(17) 8107 (2008) https://doi.org/10.1016/j.jcp.2008.05.012
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
François Bouchut and Tomás Morales de Luna ESAIM: Mathematical Modelling and Numerical Analysis 42(4) 683 (2008) https://doi.org/10.1051/m2an:2008019
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods
Godunov method for nonconservative hyperbolic systems
María Luz Muñoz-Ruiz and Carlos Parés ESAIM: Mathematical Modelling and Numerical Analysis 41(1) 169 (2007) https://doi.org/10.1051/m2an:2007011
WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE
MANUEL J. CASTRO, ALBERTO PARDO MILANÉS and CARLOS PARÉS Mathematical Models and Methods in Applied Sciences 17(12) 2055 (2007) https://doi.org/10.1142/S021820250700256X
Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances
François Bouchut Edited Series on Advances in Nonlinear Science and Complexity, Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2 189 (2007) https://doi.org/10.1016/S1574-6909(06)02004-1
Finite-Volume Solvers for a Multilayer Saint-Venant System
Emmanuel Audusse and Marie-Odile Bristeau International Journal of Applied Mathematics and Computer Science 17(3) 311 (2007) https://doi.org/10.2478/v10006-007-0025-0
Two-layer shallow water computation of mud flow intrusions into quiescent water
Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar
Manuel J. Castro, José A. García-Rodríguez, José M. González-Vida, Jorge Macías and Carlos Parés Advances in Engineering Software 38(6) 386 (2007) https://doi.org/10.1016/j.advengsoft.2006.09.012
On Well‐Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems
M. J. Castro Díaz, T. Chacón Rebollo, E. D. Fernández‐Nieto and Carlos Parés SIAM Journal on Scientific Computing 29(3) 1093 (2007) https://doi.org/10.1137/040607642
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
NUMERICAL TREATMENT OF WET/DRY FRONTS IN SHALLOW FLOWS WITH A MODIFIED ROE SCHEME
MANUEL J. CASTRO, JOSÉ M. GONZÁLEZ-VIDA and CARLOS PARÉS Mathematical Models and Methods in Applied Sciences 16(06) 897 (2006) https://doi.org/10.1142/S021820250600139X
CONSERVATION LAWS FOR ONE-DIMENSIONAL SHALLOW WATER MODELS FOR ONE AND TWO-LAYER FLOWS
A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows
M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida and C. Parés Computer Methods in Applied Mechanics and Engineering 195(19-22) 2788 (2006) https://doi.org/10.1016/j.cma.2005.07.007
The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems
Numerical simulation of two-layer shallow water flows through channels with irregular geometry
Manuel J. Castro, José A. Garcı́a-Rodrı́guez, José M. González-Vida, et al. Journal of Computational Physics 195(1) 202 (2004) https://doi.org/10.1016/j.jcp.2003.08.035
Extension of ENO and WENO schemes to one-dimensional sediment transport equations
A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions
Manuel J. Castro, Jorge Macı́as, Carlos Parés, Jose A. Garcı́a-Rodrı́guez and Elena Vázquez-Cendón Communications in Nonlinear Science and Numerical Simulation 9(2) 241 (2004) https://doi.org/10.1016/S1007-5704(03)00115-1
On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
Mathematical and Numerical Aspects of Wave Propagation WAVES 2003
M. J. Castro, J. A. García-Rodríguez, J. M. González-Vida, et al. Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 529 (2003) https://doi.org/10.1007/978-3-642-55856-6_85
A Godunov method for the computation of erosional shallow water transients
L. Fraccarollo, H. Capart and Y. Zech International Journal for Numerical Methods in Fluids 41(9) 951 (2003) https://doi.org/10.1002/fld.475
On an one-dimensional bi-layer shallow-water problem