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Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos Parés SIAM Journal on Numerical Analysis 51(3) 1371 (2013) https://doi.org/10.1137/110845379
High order exactly well-balanced numerical methods for shallow water systems
Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties
Lucas O. Müller and Eleuterio F. Toro International Journal for Numerical Methods in Biomedical Engineering 29(12) 1388 (2013) https://doi.org/10.1002/cnm.2580
Unsteady compressible flow in ducts with varying cross-section: Comparison between the nonconservative Euler system and the axisymmetric flow model
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
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
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
A Well-Balanced Symplecticity-Preserving Gas-Kinetic Scheme for Hydrodynamic Equations under Gravitational Field
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
A Duality Method for Sediment Transport Based on a Modified Meyer-Peter & Müller Model
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
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
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System
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
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
Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes
M.J. Castro Dı´az, E.D. Fernández-Nieto, A.M. Ferreiro and C. Parés Computer Methods in Applied Mechanics and Engineering 198(33-36) 2520 (2009) https://doi.org/10.1016/j.cma.2009.03.001
Two-Layer Shallow Water System: A Relaxation Approach
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
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
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
ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows
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
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
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
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
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 numerical study of a particular non-conservative hyperbolic problem
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
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
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
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
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
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
WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE
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
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
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
High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
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
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