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An MPI-CUDA implementation of an improved Roe method for two-layer shallow water systems
Marc de la Asunción, José M. Mantas, Manuel J. Castro and E.D. Fernández-Nieto Journal of Parallel and Distributed Computing 72(9) 1065 (2012) https://doi.org/10.1016/j.jpdc.2011.07.012
Restoration of the contact surface in FORCE-type centred schemes II: Non-conservative one- and two-layer two-dimensional shallow water equations
A mass-conservative centered finite volume model for solving two-dimensional two-layer shallow water equations for fluid mud propagation over varying topography and dry areas
Central Schemes for Nonconservative Hyperbolic Systems
M. J. Castro, Carlos Parés, Gabriella Puppo and Giovanni Russo SIAM Journal on Scientific Computing 34(5) B523 (2012) https://doi.org/10.1137/110828873
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
M. J. Castro-Díaz, E. D. Fernández-Nieto, J. M. González-Vida and C. Parés-Madroñal Journal of Scientific Computing 48(1-3) 16 (2011) https://doi.org/10.1007/s10915-010-9427-5
A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Model
Numerical solution of the discontinuous-bottom Shallow-water Equations with hydrostatic pressure distribution at the step
Luca Cozzolino, Renata Della Morte, Carmine Covelli, Giuseppe Del Giudice and Domenico Pianese Advances in Water Resources 34(11) 1413 (2011) https://doi.org/10.1016/j.advwatres.2011.07.009
An accurate and efficient semi‐implicit method for section‐averaged free‐surface flow modelling
G. Rosatti, L. Bonaventura, A. Deponti and G. Garegnani International Journal for Numerical Methods in Fluids 65(4) 448 (2011) https://doi.org/10.1002/fld.2191
Hyperconcentrated 1D Shallow Flows on Fixed Bed with Geometrical Source Term Due to a Bottom Step
Computational Science and High Performance Computing IV
Michael Dudzinski and Mária Lukáčová-Medviďová Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Computational Science and High Performance Computing IV 115 121 (2011) https://doi.org/10.1007/978-3-642-17770-5_10
A Well-Balanced Symplecticity-Preserving Gas-Kinetic Scheme for Hydrodynamic Equations under Gravitational Field
Numerical Mathematics and Advanced Applications 2009
T. Morales de Morales de Luna, M. J. Castro Díaz and C. Parés Madroñal Numerical Mathematics and Advanced Applications 2009 655 (2010) https://doi.org/10.1007/978-3-642-11795-4_70
Dispersive nonlinear shallow-water equations: some preliminary numerical results
AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL
JEAN DE DIEU ZABSONRÉ, CARINE LUCAS and ENRIQUE FERNÁNDEZ-NIETO Mathematical Models and Methods in Applied Sciences 19(03) 477 (2009) https://doi.org/10.1142/S0218202509003504
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
M. J. Castro, E. D. Fernández-Nieto, A. M. Ferreiro, J. A. García-Rodríguez and C. Parés Journal of Scientific Computing 39(1) 67 (2009) https://doi.org/10.1007/s10915-008-9250-4
A MUSTA Scheme for a Nonconservative Two-Fluid Model
Svend Tollak Munkejord, Steinar Evje and Tore FlÅtten SIAM Journal on Scientific Computing 31(4) 2587 (2009) https://doi.org/10.1137/080719273
Central-Upwind Schemes for Two-Layer Shallow Water Equations
Simulation of shallow-water systems using graphics processing units
Miguel Lastra, José M. Mantas, Carlos Ureña, Manuel J. Castro and José A. García-Rodríguez Mathematics and Computers in Simulation 80(3) 598 (2009) https://doi.org/10.1016/j.matcom.2009.09.012
A central scheme for shallow water flows along channels with irregular geometry
D. Bresch, M. J. C. Díaz, E. D. Fernández-Nieto, A. M. Ferreiro and A. Mangeney Hyperbolic Problems: Theory, Numerics, Applications 247 (2008) https://doi.org/10.1007/978-3-540-75712-2_20
Progress in Industrial Mathematics at ECMI 2006
M. Castro Díaz, E. D. Fernñndez Nieto and A. Ferreiro Ferreiro Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2006 12 346 (2008) https://doi.org/10.1007/978-3-540-71992-2_50
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods
A new Savage–Hutter type model for submarine avalanches and generated tsunami
E.D. Fernández-Nieto, F. Bouchut, D. Bresch, M.J. Castro Díaz and A. Mangeney Journal of Computational Physics 227(16) 7720 (2008) https://doi.org/10.1016/j.jcp.2008.04.039
Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam break of Aznalcóllar
M.J. Castro Díaz, T. Chacón Rebollo, E.D. Fernández-Nieto, J.M. González Vida and C. Parés Computer Methods in Applied Mechanics and Engineering 197(45-48) 3932 (2008) https://doi.org/10.1016/j.cma.2008.03.026
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
A numerical study of a particular non-conservative hyperbolic problem
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
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 consistent intermediate wave speed for a well-balanced HLLC solver
Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
Manuel Castro, José M. Gallardo, Juan A. López-GarcÍa and Carlos Parés SIAM Journal on Numerical Analysis 46(2) 1012 (2008) https://doi.org/10.1137/060674879
Progress in Industrial Mathematics at ECMI 2006
M. J. Castro, A. M. Ferreiro, J. A. García, J. M. González and C. Parés Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2006 12 356 (2008) https://doi.org/10.1007/978-3-540-71992-2_52
Finite Volume Simulation of the Geostrophic Adjustment in a Rotating Shallow-Water System
Manuel J. Castro, Juan Antonio López and Carlos Parés SIAM Journal on Scientific Computing 31(1) 444 (2008) https://doi.org/10.1137/070707166
Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations
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
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
Modèles Saint-Venant bicouche: application à la simulation du transport de polluants
Manuel J. Castro, Ana M. Ferreiro-Ferreiro, José A. García-Rodríguez, José M. González-Vida and Carlos Parés La Houille Blanche 93(5) 85 (2007) https://doi.org/10.1051/lhb:2007065
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
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
High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
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
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
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
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