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Ernesto Pimentel‐García, Manuel J. Castro, Christophe Chalons and Carlos Parés Numerical Methods for Partial Differential Equations 40(6) (2024) https://doi.org/10.1002/num.23133
Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: Global flux quadrature and cell entropy correction
A well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids
Alessia Del Grosso, Manuel J. Castro, Agnes Chan, Gérard Gallice, Raphaël Loubère and Pierre-Henri Maire Journal of Computational Physics 503 112829 (2024) https://doi.org/10.1016/j.jcp.2024.112829
The exact Riemann Solver to the Shallow Water equations for natural channels with bottom steps
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations
F. Fambri, E. Zampa, S. Busto, L. Río-Martín, F. Hindenlang, E. Sonnendrücker and M. Dumbser Journal of Computational Physics 493 112493 (2023) https://doi.org/10.1016/j.jcp.2023.112493
A general vertical decomposition of Euler equations: Multilayer-moment models
Efficient GPU Implementation of Multidimensional Incomplete Riemann Solvers for Hyperbolic Nonconservative Systems: Applications to Shallow Water Systems with Topography and Dry Areas
In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension
Ernesto Pimentel-García, Manuel J. Castro, Christophe Chalons, Tomás Morales de Luna and Carlos Parés Journal of Computational Physics 459 111152 (2022) https://doi.org/10.1016/j.jcp.2022.111152
Novel variable reconstruction and friction term discretisation schemes for hydrodynamic modelling of overland flow and surface water flooding
Numerical modeling of two dimensional non-capacity model for sediment transport by an unstructured finite volume method with a new discretization of the source term
A flux‐vector splitting scheme for the shallow water equations extended to high‐order on unstructured meshes
Eleuterio F. Toro, Cristòbal E. Castro, Davide Vanzo and Annunziato Siviglia International Journal for Numerical Methods in Fluids 94(10) 1679 (2022) https://doi.org/10.1002/fld.5099
A POD-based ROM strategy for the prediction in time of advection-dominated problems
A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms
Christophe Berthon, Solène Bulteau, Françoise Foucher, Meissa M'Baye and Victor Michel-Dansac SIAM Journal on Scientific Computing 44(4) A2506 (2022) https://doi.org/10.1137/21M1429230
C. R. Jisha and A. Govindarajan 2516 170017 (2022) https://doi.org/10.1063/5.0108730
Numerical Approximation of Hyperbolic Systems of Conservation Laws
Edwige Godlewski and Pierre-Arnaud Raviart Applied Mathematical Sciences, Numerical Approximation of Hyperbolic Systems of Conservation Laws 118 627 (2021) https://doi.org/10.1007/978-1-0716-1344-3_7
On Thermodynamically Compatible Finite Volume Methods and Path-Conservative ADER Discontinuous Galerkin Schemes for Turbulent Shallow Water Flows
On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems
Ernesto Pimentel-García, Carlos Parés, Manuel J. Castro and Julian Koellermeier Applied Mathematics and Computation 388 125544 (2021) https://doi.org/10.1016/j.amc.2020.125544
Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems
Kleiton A. Schneider, José M. Gallardo, Dinshaw S. Balsara, Boniface Nkonga and Carlos Parés Journal of Computational Physics 444 110547 (2021) https://doi.org/10.1016/j.jcp.2021.110547
Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape
Recent Advances in Numerical Methods for Hyperbolic PDE Systems
P. Poullet, P. Ramsamy and M. Ricchiuto SEMA SIMAI Springer Series, Recent Advances in Numerical Methods for Hyperbolic PDE Systems 28 193 (2021) https://doi.org/10.1007/978-3-030-72850-2_9
Recent Advances in Numerical Methods for Hyperbolic PDE Systems
José M. Gallardo, Manuel J. Castro and Antonio Marquina SEMA SIMAI Springer Series, Recent Advances in Numerical Methods for Hyperbolic PDE Systems 28 3 (2021) https://doi.org/10.1007/978-3-030-72850-2_1
A unified object-oriented framework for CPU+GPU explicit hyperbolic solvers
A dynamic multilayer shallow water model for polydisperse sedimentation
Raimund Bürger, Enrique D. Fernández-Nieto and Víctor Osores ESAIM: Mathematical Modelling and Numerical Analysis 53(4) 1391 (2019) https://doi.org/10.1051/m2an/2019032
Path-conservative central-upwind schemes for nonconservative hyperbolic systems
Manuel Jesús Castro Díaz, Alexander Kurganov and Tomás Morales de Luna ESAIM: Mathematical Modelling and Numerical Analysis 53(3) 959 (2019) https://doi.org/10.1051/m2an/2018077
2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization
Shape Optimization, Homogenization and Optimal Control
Mouhamadou A. M. T. Baldé and Diaraf Seck International Series of Numerical Mathematics, Shape Optimization, Homogenization and Optimal Control 169 165 (2018) https://doi.org/10.1007/978-3-319-90469-6_9
Reprint of: Well-balanced methods for the shallow water equations in spherical coordinates
Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity
Elena Gaburro, Manuel J Castro and Michael Dumbser Monthly Notices of the Royal Astronomical Society 477(2) 2251 (2018) https://doi.org/10.1093/mnras/sty542
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
M.J. Castro, T. Morales de Luna and C. Parés Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 131 (2017) https://doi.org/10.1016/bs.hna.2016.10.002
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems
M. J. Castro, C. Escalante and T. Morales de Luna Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems 200 119 (2017) https://doi.org/10.1007/978-3-319-57394-6_13
A multi well-balanced scheme for the shallow water MHD system with topography
Data-driven Modeling of the Solar Corona by a New Three-dimensional Path-conservative Osher–Solomon MHD Model
Xueshang Feng, Caixia Li, Changqing Xiang, Man Zhang, HuiChao Li and Fengsi Wei The Astrophysical Journal Supplement Series 233(1) 10 (2017) https://doi.org/10.3847/1538-4365/aa957a
Well-balanced methods for the shallow water equations in spherical coordinates
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
E. D. Fernández-Nieto Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 15 (2017) https://doi.org/10.1007/978-3-319-57397-7_2
Well balancing of the SWE schemes for moving-water steady flows
A two-phase shallow debris flow model with energy balance
F. Bouchut, E.D. Fernández-Nieto, A. Mangeney and G. Narbona-Reina ESAIM: Mathematical Modelling and Numerical Analysis 49(1) 101 (2015) https://doi.org/10.1051/m2an/2014026
A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows
M.J. Castro Díaz, E.D. Fernández-Nieto, G. Narbona-Reina and M. de la Asunción Journal of Computational Physics 262 172 (2014) https://doi.org/10.1016/j.jcp.2013.12.059
A Riemann problem solution methodology for a class of evolutionary mixture equations with an arbitrary number of components
A global multiscale mathematical model for the human circulation with emphasis on the venous system
Lucas O. Müller and Eleuterio F. Toro International Journal for Numerical Methods in Biomedical Engineering 30(7) 681 (2014) https://doi.org/10.1002/cnm.2622
On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems
Relation between PVM schemes and simple Riemann solvers
Tomás Morales de Luna, Manuel J. Castro Díaz and Carlos Parés Numerical Methods for Partial Differential Equations 30(4) 1315 (2014) https://doi.org/10.1002/num.21871
A Class of Incomplete Riemann Solvers Based on Uniform Rational Approximations to the Absolute Value Function
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
High order exactly well-balanced numerical methods for shallow water systems
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
Formal derivation of a bilayer model coupling shallow water and Reynolds lubrication equations: evolution of a thin pollutant layer over water
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
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 Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
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