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Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes

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FORCE schemes on moving unstructured meshes for hyperbolic systems

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2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization

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Solving shallow-water systems in 2D domains using Finite Volume methods and multimedia SSE instructions

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Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts

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Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws

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Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues

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AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL

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Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis

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A comparison between bottom-discontinuity numerical treatments in the DG framework

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An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes

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Efficient multilayer shallow-water simulation system based on GPUs

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NUMERICAL TREATMENT OF WET/DRY FRONTS IN SHALLOW FLOWS WITH A MODIFIED ROE SCHEME

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WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE

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On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems

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Well-balanced methods for the shallow water equations in spherical coordinates

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Two-Dimensional Simulation of Rarefied Gas Flows Using Quadrature-Based Moment Equations

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Reprint of: Well-balanced methods for the shallow water equations in spherical coordinates

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Well balancing of the SWE schemes for moving-water steady flows

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A well-balanced FV scheme for compound channels with complex geometry and movable bed

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Water Resources Research 51 (8) 6564 (2015)
DOI: 10.1002/2014WR016584
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A multi well-balanced scheme for the shallow water MHD system with topography

François Bouchut and Xavier Lhébrard
Numerische Mathematik 136 (4) 875 (2017)
DOI: 10.1007/s00211-017-0865-y
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A Roe-like numerical method for weakly hyperbolic systems of equations in conservation and non-conservation form

Timothy A. Smith, David J. Petty and Carlos Pantano
Journal of Computational Physics 316 117 (2016)
DOI: 10.1016/j.jcp.2016.04.006
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Approximate Osher–Solomon schemes for hyperbolic systems

Manuel J. Castro, José M. Gallardo and Antonio Marquina
Applied Mathematics and Computation 272 347 (2016)
DOI: 10.1016/j.amc.2015.06.104
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Numerical methods for nonconservative hyperbolic systems: a theoretical framework.

Carlos Parés
SIAM Journal on Numerical Analysis 44 (1) 300 (2006)
DOI: 10.1137/050628052
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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)
DOI: 10.1093/mnras/sty542
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Moving mesh version of wave propagation algorithm based on augmented Riemann solver

Mina Bagherpoorfard and Ali R. Soheili
Applied Mathematics and Computation 375 125087 (2020)
DOI: 10.1016/j.amc.2020.125087
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The Riemann problem for the shallow water equations with discontinuous topography: The wet–dry case

Carlos Parés and Ernesto Pimentel
Journal of Computational Physics 378 344 (2019)
DOI: 10.1016/j.jcp.2018.11.019
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Data-driven Modeling of the Solar Corona by a New Three-dimensional Path-conservative Osher–Solomon MHD Model

Xueshang Feng, Caixia Li, Changqing Xiang, et al.
The Astrophysical Journal Supplement Series 233 (1) 10 (2017)
DOI: 10.3847/1538-4365/aa957a
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An energy concept for macroscopic traffic flow modelling

Abdelaziz Nakrachi, Said Hayat and Dumitru Popescu
European Transport Research Review 4 (2) 57 (2012)
DOI: 10.1007/s12544-012-0070-0
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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)
DOI: 10.1007/978-3-540-71992-2_52
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Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant

E. D. Fernández-Nieto and G. Narbona-Reina
Journal of Scientific Computing 36 (2) 193 (2008)
DOI: 10.1007/s10915-008-9185-9
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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)
DOI: 10.1007/s10915-008-9250-4
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An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

Jingming Hou, Qiuhua Liang, Hongbin Zhang and Reinhard Hinkelmann
Environmental Modelling & Software 66 131 (2015)
DOI: 10.1016/j.envsoft.2014.12.007
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Dispersive nonlinear shallow-water equations: some preliminary numerical results

Giovanna Grosso, Matteo Antuono and Maurizio Brocchini
Journal of Engineering Mathematics 67 (1-2) 71 (2010)
DOI: 10.1007/s10665-009-9328-5
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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)
DOI: 10.1002/fld.2191
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Numerical Mathematics and Advanced Applications

M. J. Castro, J. A. García, J. M. González and C. Parés
Numerical Mathematics and Advanced Applications 288 (2006)
DOI: 10.1007/978-3-540-34288-5_22
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Numerical Mathematics and Advanced Applications

M. J. Castro-Díaz, E. D. Fernández-Nieto and A. M. Ferreiro
Numerical Mathematics and Advanced Applications 190 (2006)
DOI: 10.1007/978-3-540-34288-5_11
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Hyperbolic Problems: Theory, Numerics, Applications

C. Parés
Hyperbolic Problems: Theory, Numerics, Applications 817 (2008)
DOI: 10.1007/978-3-540-75712-2_84
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Hyperbolic Problems: Theory, Numerics, Applications

J. M. Gallardo, M. Castro, C. Parés and J. M. González-Vida
Hyperbolic Problems: Theory, Numerics, Applications 259 (2008)
DOI: 10.1007/978-3-540-75712-2_21
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Hyperbolic Problems: Theory, Numerics, Applications

D. Bresch, M. J. C. Díaz, E. D. Fernández-Nieto, A. M. Ferreiro and A. Mangeney
Hyperbolic Problems: Theory, Numerics, Applications 247 (2008)
DOI: 10.1007/978-3-540-75712-2_20
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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)
DOI: 10.1007/978-3-540-71992-2_50
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Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity

Nino Krvavica, Miran Tuhtan and Gordan Jelenić
Advances in Water Resources 122 187 (2018)
DOI: 10.1016/j.advwatres.2018.10.017
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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)
DOI: 10.1007/978-3-642-11795-4_70
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Numerical Mathematics and Advanced Applications 2009

M. L. Muñoz-Ruiz, C. Parés and M. J. Castro Díaz
Numerical Mathematics and Advanced Applications 2009 675 (2010)
DOI: 10.1007/978-3-642-11795-4_72
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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)
DOI: 10.1007/978-3-642-17770-5_10
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Derivation of a Multilayer Approach to Model Suspended Sediment Transport: Application to Hyperpycnal and Hypopycnal Plumes

T. Morales de Luna, E.D. Fernández Nieto and M. J. Castro Díaz
Communications in Computational Physics 22 (5) 1439 (2017)
DOI: 10.4208/cicp.OA-2016-0215
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Numerical Study of Partially Conservative Moment Equations in Kinetic Theory

Julian Koellermeier and Manuel Torrilhon
Communications in Computational Physics 21 (4) 981 (2017)
DOI: 10.4208/cicp.OA-2016-0053
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Shock Profiles for the Shallow-Water Exner Models

C. Berthon, B. Boutin and R. Turpault
Advances in Applied Mathematics and Mechanics 7 (3) 267 (2015)
DOI: 10.4208/aamm.2013.m331
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Formal derivation of a bilayer model coupling shallow water and Reynolds lubrication equations: evolution of a thin pollutant layer over water

E. D. FERNÁNDEZ-NIETO, G. NARBONA-REINA and J. D. ZABSONRÉ
European Journal of Applied Mathematics 24 (6) 803 (2013)
DOI: 10.1017/S095679251300020X
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Edwige Godlewski and Pierre-Arnaud Raviart
118 627 (2021)
DOI: 10.1007/978-1-0716-1344-3_7
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Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions

Nino Krvavica
Advances in Water Resources 137 103508 (2020)
DOI: 10.1016/j.advwatres.2020.103508
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Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws

Manuel J. Castro and Carlos Parés
Journal of Scientific Computing 82 (2) (2020)
DOI: 10.1007/s10915-020-01149-5
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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)
DOI: 10.1051/m2an/2019032
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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)
DOI: 10.1051/m2an/2018077
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A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

Friedemann Kemm, Elena Gaburro, Ferdinand Thein and Michael Dumbser
Computers & Fluids 204 104536 (2020)
DOI: 10.1016/j.compfluid.2020.104536
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A unified object-oriented framework for CPU+GPU explicit hyperbolic solvers

Daniel A.S. Conde, Ricardo B. Canelas and Rui M.L. Ferreira
Advances in Engineering Software 148 102802 (2020)
DOI: 10.1016/j.advengsoft.2020.102802
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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)
DOI: 10.1051/lhb:2007065
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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)
DOI: 10.1007/978-3-030-72850-2_1
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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)
DOI: 10.1007/978-3-030-72850-2_9
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M.J. Castro, J.M. Gallardo, M.L. Muñoz and C. Parés
662 (2006)
DOI: 10.1007/978-3-540-34288-5_64
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Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopes

Stelian Ion, Dorin Marinescu and Stefan-Gicu Cruceanu
Applied Numerical Mathematics 172 67 (2022)
DOI: 10.1016/j.apnum.2021.09.019
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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)
DOI: 10.1016/j.jcp.2021.110547
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A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers

S. Busto and M. Dumbser
Applied Numerical Mathematics 175 108 (2022)
DOI: 10.1016/j.apnum.2022.02.005
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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

S. Jelti and M. Boulerhcha
Mathematics and Computers in Simulation 197 253 (2022)
DOI: 10.1016/j.matcom.2022.02.012
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Steady states and well-balanced schemes for shallow water moment equations with topography

Julian Koellermeier and Ernesto Pimentel-García
Applied Mathematics and Computation 427 127166 (2022)
DOI: 10.1016/j.amc.2022.127166
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Novel variable reconstruction and friction term discretisation schemes for hydrodynamic modelling of overland flow and surface water flooding

Jiaheng Zhao and Qiuhua Liang
Advances in Water Resources 163 104187 (2022)
DOI: 10.1016/j.advwatres.2022.104187
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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)
DOI: 10.1016/j.jcp.2022.111152
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Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape

C. Escalante, M.J. Castro and M. Semplice
Applied Mathematics and Computation 398 125993 (2021)
DOI: 10.1016/j.amc.2021.125993
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High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves

C. Bassi, S. Busto and M. Dumbser
Applied Numerical Mathematics 158 236 (2020)
DOI: 10.1016/j.apnum.2020.08.005
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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 (2022)
DOI: 10.1002/fld.5099
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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

Alberto Canestrelli, Sergio Fagherazzi and Stefano Lanzoni
Advances in Water Resources 40 54 (2012)
DOI: 10.1016/j.advwatres.2012.01.009
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Efficient GPU Implementation of Multidimensional Incomplete Riemann Solvers for Hyperbolic Nonconservative Systems: Applications to Shallow Water Systems with Topography and Dry Areas

Kleiton A. Schneider, José M. Gallardo and Cipriano Escalante
Journal of Scientific Computing 92 (2) (2022)
DOI: 10.1007/s10915-022-01880-1
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