EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 38 5 (2004) 821-852 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: preserving isentropic steady solutions

Christophe Berthon, Victor Michel-Dansac and Andrea Thomann
Mathematics of Computation (2025)
https://doi.org/10.1090/mcom/4088

Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for two-layer shallow water equations

Jiahui Zhang, Yinhua Xia and Yan Xu
Journal of Computational Physics 520 113473 (2025)
https://doi.org/10.1016/j.jcp.2024.113473

Combination of intrusive POD-based reduced-order models and augmented Riemann solvers applied to unsteady 2D shallow water equations

P. Solán-Fustero, J.L. Gracia, A. Navas-Montilla and P. García-Navarro
Computer Methods in Applied Mechanics and Engineering 436 117702 (2025)
https://doi.org/10.1016/j.cma.2024.117702

A multilayer shallow water model for tsunamis and coastal forest interaction

Raimund Bürger, Enrique D. Fernández-Nieto and Jorge Moya
ESAIM: Mathematical Modelling and Numerical Analysis 59 (2) 1113 (2025)
https://doi.org/10.1051/m2an/2025017

Uncertainty Quantification and Sensitivity Analysis for Non‐invasive Model‐Based Instantaneous Wave‐Free Ratio Prediction

Caterina Dalmaso, Fredrik Eikeland Fossan, Anders Tjellaug Bråten and Lucas Omar Müller
International Journal for Numerical Methods in Biomedical Engineering 41 (1) (2025)
https://doi.org/10.1002/cnm.3898

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

Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: Global flux quadrature and cell entropy correction

Yogiraj Mantri, Philipp Öffner and Mario Ricchiuto
Journal of Computational Physics 498 112673 (2024)
https://doi.org/10.1016/j.jcp.2023.112673

High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method

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

A Well-Balanced Active Flux Method for the Shallow Water Equations with Wetting and Drying

Wasilij Barsukow and Jonas P. Berberich
Communications on Applied Mathematics and Computation 6 (4) 2385 (2024)
https://doi.org/10.1007/s42967-022-00241-x

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

J. Garres-Díaz, C. Escalante, T. Morales de Luna and M.J. Castro Díaz
Applied Numerical Mathematics 183 236 (2023)
https://doi.org/10.1016/j.apnum.2022.09.004

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)
https://doi.org/10.1016/j.matcom.2022.02.012

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

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)
https://doi.org/10.1016/j.apnum.2021.09.019

A POD-based ROM strategy for the prediction in time of advection-dominated problems

P. Solán-Fustero, J.L. Gracia, A. Navas-Montilla and P. García-Navarro
Journal of Computational Physics 471 111672 (2022)
https://doi.org/10.1016/j.jcp.2022.111672

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

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)
https://doi.org/10.1007/s10915-022-01880-1

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

Jiaheng Zhao and Qiuhua Liang
Advances in Water Resources 163 104187 (2022)
https://doi.org/10.1016/j.advwatres.2022.104187

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)
https://doi.org/10.1016/j.amc.2022.127166

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)
https://doi.org/10.1016/j.apnum.2022.02.005

On Thermodynamically Compatible Finite Volume Methods and Path-Conservative ADER Discontinuous Galerkin Schemes for Turbulent Shallow Water Flows

Saray Busto, Michael Dumbser, Sergey Gavrilyuk and Kseniya Ivanova
Journal of Scientific Computing 88 (1) (2021)
https://doi.org/10.1007/s10915-021-01521-z

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

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

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

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

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

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)
https://doi.org/10.1016/j.amc.2021.125993

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)
https://doi.org/10.1016/j.advwatres.2020.103508

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)
https://doi.org/10.1016/j.amc.2020.125087

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)
https://doi.org/10.1016/j.apnum.2020.08.005

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)
https://doi.org/10.1016/j.compfluid.2020.104536

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)
https://doi.org/10.1016/j.jcp.2018.11.019

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

C. Escalante, M. Dumbser and M.J. Castro
Journal of Computational Physics 394 385 (2019)
https://doi.org/10.1016/j.jcp.2019.05.035

FORCE schemes on moving unstructured meshes for hyperbolic systems

Walter Boscheri, Michael Dumbser and Maurizio Righetti
Computers & Mathematics with Applications 78 (2) 362 (2019)
https://doi.org/10.1016/j.camwa.2018.09.008

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

E.D. Fernández-Nieto, J. Garres-Díaz, A. Mangeney and G. Narbona-Reina
Journal of Computational Physics 356 192 (2018)
https://doi.org/10.1016/j.jcp.2017.11.038

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)
https://doi.org/10.1016/j.advwatres.2018.10.017

A generalized Rusanov method for the Baer‐Nunziato equations with application to DDT processes in condensed porous explosives

Igor Menshov and Alexey Serezhkin
International Journal for Numerical Methods in Fluids 86 (5) 346 (2018)
https://doi.org/10.1002/fld.4419

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

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

Efficient multilayer shallow-water simulation system based on GPUs

Miguel Lastra, Manuel J. Castro Díaz, Carlos Ureña and Marc de la Asunción
Mathematics and Computers in Simulation 148 48 (2018)
https://doi.org/10.1016/j.matcom.2017.11.008

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

Julian Koellermeier and Manuel Torrilhon
Multiscale Modeling & Simulation 16 (2) 1059 (2018)
https://doi.org/10.1137/17M1147548

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

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

High Order Direct Arbitrary-Lagrangian–Eulerian (ALE) Finite Volume Schemes for Hyperbolic Systems on Unstructured Meshes

Walter Boscheri
Archives of Computational Methods in Engineering 24 (4) 751 (2017)
https://doi.org/10.1007/s11831-016-9188-x

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

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)
https://doi.org/10.4208/cicp.OA-2016-0215

Numerical Study of Partially Conservative Moment Equations in Kinetic Theory

Julian Koellermeier and Manuel Torrilhon
Communications in Computational Physics 21 (4) 981 (2017)
https://doi.org/10.4208/cicp.OA-2016-0053

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

Valerio Caleffi, Alessandro Valiani and Gang Li
Applied Mathematical Modelling 40 (17-18) 7516 (2016)
https://doi.org/10.1016/j.apm.2015.09.025

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)
https://doi.org/10.1016/j.jcp.2016.04.006

Approximate Osher–Solomon schemes for hyperbolic systems

Manuel J. Castro, José M. Gallardo and Antonio Marquina
Applied Mathematics and Computation 272 347 (2016)
https://doi.org/10.1016/j.amc.2015.06.104

Second order discontinuous Galerkin scheme for compound natural channels with movable bed. Applications for the computation of rating curves

Lorenzo Minatti, Pina Nicoletta De Cicco and Luca Solari
Advances in Water Resources 93 89 (2016)
https://doi.org/10.1016/j.advwatres.2015.06.007

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

Olindo Zanotti and Michael Dumbser
Computational Astrophysics and Cosmology 3 (1) (2016)
https://doi.org/10.1186/s40668-015-0014-x

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

L. Minatti
Water Resources Research 51 (8) 6564 (2015)
https://doi.org/10.1002/2014WR016584

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)
https://doi.org/10.1016/j.envsoft.2014.12.007

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)
https://doi.org/10.4208/aamm.2013.m331

An efficient splitting technique for two-layer shallow-water model

Christophe Berthon, Françoise Foucher and Tomás Morales
Numerical Methods for Partial Differential Equations 31 (5) 1396 (2015)
https://doi.org/10.1002/num.21949

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

C. Sánchez-Linares, M. de la Asunción, M.J. Castro, S. Mishra and J. Šukys
Applied Mathematical Modelling (2015)
https://doi.org/10.1016/j.apm.2015.03.011

Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

Qiuhua Liang, Jingming Hou and Xilin Xia
International Journal for Numerical Methods in Fluids 78 (1) 17 (2015)
https://doi.org/10.1002/fld.4005

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 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

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

One-dimensional numerical modeling of the long-term morphodynamic evolution of a tidally-dominated estuary: The Lower Fly River (Papua New Guinea)

Alberto Canestrelli, Stefano Lanzoni and Sergio Fagherazzi
Sedimentary Geology 301 107 (2014)
https://doi.org/10.1016/j.sedgeo.2013.06.009

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

E.D. Fernández-Nieto, C. Lucas, T. Morales de Luna and S. Cordier
Computers & Fluids 91 87 (2014)
https://doi.org/10.1016/j.compfluid.2013.11.031

A Class of Incomplete Riemann Solvers Based on Uniform Rational Approximations to the Absolute Value Function

Manuel J. Castro, José M. Gallardo and Antonio Marquina
Journal of Scientific Computing 60 (2) 363 (2014)
https://doi.org/10.1007/s10915-013-9800-2

A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution

E. D. Fernández-Nieto, E. H. Koné and T. Chacón Rebollo
Journal of Scientific Computing 60 (2) 408 (2014)
https://doi.org/10.1007/s10915-013-9802-0

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

High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems

Michael Dumbser, Arturo Hidalgo and Olindo Zanotti
Computer Methods in Applied Mechanics and Engineering 268 359 (2014)
https://doi.org/10.1016/j.cma.2013.09.022

A Riemann problem solution methodology for a class of evolutionary mixture equations with an arbitrary number of components

M.W. Crochet and K.A. Gonthier
Applied Numerical Mathematics 76 145 (2014)
https://doi.org/10.1016/j.apnum.2013.09.004

High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: Applications to compressible multi-phase flows

Michael Dumbser and Walter Boscheri
Computers & Fluids 86 405 (2013)
https://doi.org/10.1016/j.compfluid.2013.07.024

A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment

Jingming Hou, Qiuhua Liang, Franz Simons and Reinhard Hinkelmann
Advances in Water Resources 52 107 (2013)
https://doi.org/10.1016/j.advwatres.2012.08.003

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

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)
https://doi.org/10.1017/S095679251300020X

A multilayer shallow water system for polydisperse sedimentation

E.D. Fernández-Nieto, E.H. Koné, T. Morales de Luna and R. Bürger
Journal of Computational Physics 238 281 (2013)
https://doi.org/10.1016/j.jcp.2012.12.008

High order exactly well-balanced numerical methods for shallow water systems

M.J. Castro Díaz, J.A. López-García and Carlos Parés
Journal of Computational Physics 246 242 (2013)
https://doi.org/10.1016/j.jcp.2013.03.033

Reliability of first order numerical schemes for solving shallow water system over abrupt topography

T. Morales de Luna, M.J. Castro Díaz and C. Parés
Applied Mathematics and Computation 219 (17) 9012 (2013)
https://doi.org/10.1016/j.amc.2013.03.033

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

Marc de la Asunción, Manuel J. Castro, E.D. Fernández-Nieto, et al.
Computers & Fluids 80 441 (2013)
https://doi.org/10.1016/j.compfluid.2012.01.012

Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources

M.W. Crochet and K.A. Gonthier
Journal of Computational Physics 255 266 (2013)
https://doi.org/10.1016/j.jcp.2013.08.010

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

Two-dimensional simulation of debris flows over mobile bed: Enhancing the TRENT2D model by using a well-balanced Generalized Roe-type solver

Giorgio Rosatti and Lorenzo Begnudelli
Computers & Fluids 71 179 (2013)
https://doi.org/10.1016/j.compfluid.2012.10.006

A closure-independent Generalized Roe solver for free-surface, two-phase flows over mobile bed

Giorgio Rosatti and Lorenzo Begnudelli
Journal of Computational Physics 255 362 (2013)
https://doi.org/10.1016/j.jcp.2013.08.020

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

M. Dudzinski and M. Lukáčová-Medvid’ová
Journal of Computational Physics 235 82 (2013)
https://doi.org/10.1016/j.jcp.2012.10.037

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