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:

This article has been cited by the following article(s):

A numerical method for the two layer shallow water equations with dry states

Kyle T. Mandli
Ocean Modelling 72 80 (2013)
DOI: 10.1016/j.ocemod.2013.08.001
See this article

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)
DOI: 10.1002/num.21949
See this article

Finite-volume schemes for shallow-water equations

Alexander Kurganov
Acta Numerica 27 289 (2018)
DOI: 10.1017/S0962492918000028
See this article

Numerical scheme for multilayer shallow-water model in the low-Froude number regime

Martin Parisot and Jean-Paul Vila
Comptes Rendus Mathematique 352 (11) 953 (2014)
DOI: 10.1016/j.crma.2014.09.020
See this article

A new composite scheme for two-layer shallow water flows with shocks

Nouh Izem, Fayssal Benkhaldoun, Slah Sahmim, Mohammed Seaid and Mohamed Wakrim
Journal of Applied Mathematics and Computing 44 (1-2) 467 (2014)
DOI: 10.1007/s12190-013-0703-z
See this article

Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing

H. Alemi Ardakani, T.J. Bridges and M.R. Turner
Journal of Fluids and Structures 59 432 (2015)
DOI: 10.1016/j.jfluidstructs.2015.10.002
See this article

A general two-phase debris flow model

Shiva P. Pudasaini
Journal of Geophysical Research: Earth Surface 117 (F3) n/a (2012)
DOI: 10.1029/2011JF002186
See this article

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)
DOI: 10.1137/110828873
See this article

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

E. D. Fernández-Nieto, M. J. Castro Díaz and C. Parés
Journal of Scientific Computing 48 (1-3) 117 (2011)
DOI: 10.1007/s10915-011-9465-7
See this article

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)
DOI: 10.1007/s10915-010-9427-5
See this article

A discontinuous Galerkin method for two-layer shallow water equations

Nouh Izem, Mohammed Seaid and Mohamed Wakrim
Mathematics and Computers in Simulation 120 12 (2016)
DOI: 10.1016/j.matcom.2015.04.009
See this article

A compressible two-layer model for transient gas–liquid flows in pipes

Charles Demay and Jean-Marc Hérard
Continuum Mechanics and Thermodynamics 29 (2) 385 (2017)
DOI: 10.1007/s00161-016-0531-0
See this article

Three-Layer Approximation of Two-Layer Shallow Water Equations

Alina Chertock, Alexander Kurganov, Zhuolin Qu and Tong Wu
Mathematical Modelling and Analysis 18 (5) 675 (2013)
DOI: 10.3846/13926292.2013.869269
See this article

Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help

S. Cordier, M.H. Le and T. Morales de Luna
Advances in Water Resources 34 (8) 980 (2011)
DOI: 10.1016/j.advwatres.2011.05.002
See this article

Regularized Equations for Numerical Simulation of Flows in the Two-Layer Shallow Water Approximation

T. G. Elizarova and A. V. Ivanov
Computational Mathematics and Mathematical Physics 58 (5) 714 (2018)
DOI: 10.1134/S0965542518050081
See this article

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

Eirik Holm Fyhn, Karl Yngve Lervåg, Åsmund Ervik and Øivind Wilhelmsen
Physics of Fluids 31 (12) 122103 (2019)
DOI: 10.1063/1.5126168
See this article

Air entrainment in transient flows in closed water pipes : A two-layer approach

C. Bourdarias, M. Ersoy and Stéphane Gerbi
ESAIM: Mathematical Modelling and Numerical Analysis 47 (2) 507 (2013)
DOI: 10.1051/m2an/2012036
See this article

A Two-Layer Hydrostatic-Reconstruction Method for High-Resolution Solving of the Two-Layer Shallow-Water Equations over Uneven Bed Topography

Jiang Lin, Bing Mao and Xinhua Lu
Mathematical Problems in Engineering 2019 1 (2019)
DOI: 10.1155/2019/5064171
See this article

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

Y. Xing
Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 361 (2017)
DOI: 10.1016/bs.hna.2016.09.003
See this article

A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame and Jacques Sainte-Marie
ESAIM: Mathematical Modelling and Numerical Analysis 45 (1) 169 (2011)
DOI: 10.1051/m2an/2010036
See this article

A simple multi-layer finite volume solver for density-driven shallow water flows

Fayssal Benkhaldoun, Saida Sari and Mohammed Seaid
Mathematics and Computers in Simulation 99 170 (2014)
DOI: 10.1016/j.matcom.2013.04.016
See this article

Multilayer Saint-Venant equations over movable beds

Mohammed Seaid, Jacques Sainte-Marie, Fayssal Benkhaldoun and Emmanuel Audusse
Discrete and Continuous Dynamical Systems - Series B 15 (4) 917 (2011)
DOI: 10.3934/dcdsb.2011.15.917
See this article

Solution properties and approximate Riemann solvers for two-layer shallow flow models

Benoit Spinewine, Vincent Guinot, Sandra Soares-Frazão and Yves Zech
Computers & Fluids 44 (1) 202 (2011)
DOI: 10.1016/j.compfluid.2011.01.001
See this article

Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 2. Active lower layer

Journal of Fluid Mechanics 665 209 (2010)
DOI: 10.1017/S0022112010003903
See this article

A fast finite volume solver for multi-layered shallow water flows with mass exchange

Emmanuel Audusse, Fayssal Benkhaldoun, Saida Sari, Mohammed Seaid and Pablo Tassi
Journal of Computational Physics 272 23 (2014)
DOI: 10.1016/
See this article

A robust and well-balanced numerical model for solving the two-layer shallow water equations over uneven topography

Xinhua Lu, Bingjiang Dong, Bing Mao and Xiaofeng Zhang
Comptes Rendus Mécanique 343 (7-8) 429 (2015)
DOI: 10.1016/j.crme.2015.05.002
See this article

Convergence Improved Lax-Friedrichs Scheme Based Numerical Schemes and Their Applications in Solving the One-Layer and Two-Layer Shallow-Water Equations

Xinhua Lu, Bingjiang Dong, Bing Mao and Xiaofeng Zhang
Mathematical Problems in Engineering 2015 1 (2015)
DOI: 10.1155/2015/379281
See this article

An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification

F. Couderc, A. Duran and J.-P. Vila
Journal of Computational Physics 343 235 (2017)
DOI: 10.1016/
See this article

Central-Upwind Schemes for Two-Layer Shallow Water Equations

Alexander Kurganov and Guergana Petrova
SIAM Journal on Scientific Computing 31 (3) 1742 (2009)
DOI: 10.1137/080719091
See this article

Centered-Potential Regularization for the Advection Upstream Splitting Method

Martin Parisot and Jean-Paul Vila
SIAM Journal on Numerical Analysis 54 (5) 3083 (2016)
DOI: 10.1137/15M1021817
See this article

State Feedback Stabilization of the Linearized Bilayer Saint-Venant Model

Ababacar Diagne, Shuxia Tang, Mamadou Diagne and Miroslav Krstic
IFAC-PapersOnLine 49 (8) 130 (2016)
DOI: 10.1016/j.ifacol.2016.07.431
See this article

A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet–dry treatment

P. García-Navarro, A. Ramos-Pérez and S. Martínez-Aranda
Journal of Hydroinformatics (2020)
DOI: 10.2166/hydro.2020.002
See this article

Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface

Sebastien Allgeyer, Marie-Odile Bristeau, David Froger, et al.
ESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 1981 (2019)
DOI: 10.1051/m2an/2019044
See this article

Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts

J. Murillo, S. Martinez-Aranda, A. Navas-Montilla and P. García-Navarro
Journal of Hydroinformatics 22 (5) 972 (2020)
DOI: 10.2166/hydro.2020.207
See this article

A well‐balanced positivity‐preserving central‐upwind scheme for one‐dimensional blood flow models

Gerardo Hernandez‐Duenas and Guillermo Ramirez‐Santiago
International Journal for Numerical Methods in Fluids 93 (2) 369 (2021)
DOI: 10.1002/fld.4887
See this article

Control of shallow waves of two unmixed fluids by backstepping

Mamadou Diagne, Shu-Xia Tang, Ababacar Diagne and Miroslav Krstic
Annual Reviews in Control 44 211 (2017)
DOI: 10.1016/j.arcontrol.2017.09.003
See this article

Quasi-gasdynamic algorithm for numerical solution of two-layer shallow water equations

Tatiana Gennadyevna Elizarova and Aleksander Vladimirovich Ivanov
Keldysh Institute Preprints (69) 1 (2016)
DOI: 10.20948/prepr-2016-69
See this article

Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities

Christophe Berthon, Arnaud Duran, Françoise Foucher, Khaled Saleh and Jean De Dieu Zabsonré
Journal of Scientific Computing 80 (2) 924 (2019)
DOI: 10.1007/s10915-019-00961-y
See this article

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
See this article

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

Manuel Jesús Castro Diaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov
Communications in Computational Physics 16 (5) 1323 (2014)
DOI: 10.4208/cicp.180513.230514a
See this article

A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows

J. Vides, B. Braconnier, E. Audit, C. Berthon and B. Nkonga
Communications in Computational Physics 15 (1) 46 (2014)
DOI: 10.4208/cicp.060712.210313a
See this article

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
See this article

Adaptation of f-wave finite volume methods to the two-layer shallow-water equations in a moving vessel with a rigid-lid

H. Alemi Ardakani, T.J. Bridges and M.R. Turner
Journal of Computational and Applied Mathematics 296 462 (2016)
DOI: 10.1016/
See this article