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:

A semi-Lagrangian Splitting framework for the simulation of non-hydrostatic free-surface flows

Andreas Alexandris-Galanopoulos, George Papadakis and Kostas Belibassakis
Ocean Modelling 187 102290 (2024)
https://doi.org/10.1016/j.ocemod.2023.102290

A robust numerical scheme based on auxiliary interface variables and monotone-preserving reconstructions for two-layer shallow water equations with wet–dry fronts

Jian Dong and Xu Qian
Computers & Fluids 272 106193 (2024)
https://doi.org/10.1016/j.compfluid.2024.106193

High-order compact gas-kinetic scheme for two-layer shallow water equations on unstructured mesh

Fengxiang Zhao, Jianping Gan and Kun Xu
Journal of Computational Physics 498 112651 (2024)
https://doi.org/10.1016/j.jcp.2023.112651

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 (2024)
https://doi.org/10.1002/num.23133

The Navier-Stokes system with temperature and salinity for free surface flows. Numerical scheme and validation

L. Boittin, F. Bouchut, M.-O. Bristeau, A. Mangeney, J. Sainte-Marie and F. Souillé
Journal of Computational Physics 510 113065 (2024)
https://doi.org/10.1016/j.jcp.2024.113065

On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations

A. Del Grosso, M. Castro Díaz, C. Chalons and T. Morales de Luna
Applied Mathematics and Computation 442 127702 (2023)
https://doi.org/10.1016/j.amc.2022.127702

Discussion on different numerical treatments on the loss of hyperbolicity for the two-layer shallow water system

M.J. Castro Díaz, E.D. Fernández-Nieto, J. Garres-Díaz and T. Morales de Luna
Advances in Water Resources 182 104587 (2023)
https://doi.org/10.1016/j.advwatres.2023.104587

Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities

Christophe Berthon, Manuel J. Castro Díaz, Arnaud Duran, Tomás Morales de Luna and Khaled Saleh
Journal of Scientific Computing 97 (3) (2023)
https://doi.org/10.1007/s10915-023-02385-1

Flux globalization based well-balanced path-conservative central-upwind scheme for two-layer thermal rotating shallow water equations

Yangyang Cao, Alexander Kurganov, Yongle Liu and Vladimir Zeitlin
Journal of Computational Physics 474 111790 (2023)
https://doi.org/10.1016/j.jcp.2022.111790

Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for Two-Layer Thermal Rotating Shallow Water Equations

Yangyang Cao, Alexander Kurganov, Yongle Liu and Vladimir Zeitlin
SSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4089079

An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density

E. Guerrero Fernández, M. J. Castro Díaz, M. Dumbser and T. Morales de Luna
Journal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01734-2

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

An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation

Jiao Zhang, Zhangyi Mi, Wen Wang, Zhanbin Li, Huilin Wang, Qingjing Wang, Xunle Zhang and Xinchun Du
Water 14 (21) 3562 (2022)
https://doi.org/10.3390/w14213562

Fifth-order A-WENO schemes based on the path-conservative central-upwind method

Shaoshuai Chu, Alexander Kurganov and Mingye Na
Journal of Computational Physics 469 111508 (2022)
https://doi.org/10.1016/j.jcp.2022.111508

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

A fifth order WENO scheme for numerical simulation of shallow granular two-phase flow model

Omar Rabbani, Saqib Zia and Asad Rehman
Advances in Mechanical Engineering 13 (9) 168781402110452 (2021)
https://doi.org/10.1177/16878140211045240

A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows

Alia Al-Ghosoun, Nabil El Moçayd and Mohammed Seaid
Environmental Modelling & Software 144 105176 (2021)
https://doi.org/10.1016/j.envsoft.2021.105176

A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels

Gerardo Hernandez-Duenas and Jorge Balbás
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2185 (2021)
https://doi.org/10.1051/m2an/2021052

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

Efficient modeling of shallow water equations using method of lines and artificial viscosity

Mohamed M. Mousa and Wen-Xiu Ma
Modern Physics Letters B 34 (04) 2050051 (2020)
https://doi.org/10.1142/S0217984920500517

A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density

Ernesto Guerrero Fernández, Manuel Jesús Castro-Díaz and Tomás Morales de Luna
Mathematics 8 (5) 848 (2020)
https://doi.org/10.3390/math8050848

An alternative model of multicomponent diffusion based on a combination of the Maxwell-Stefan theory and continuum mechanics

Jan Franců and Jiří Mikyška
Journal of Computational Physics 400 108962 (2020)
https://doi.org/10.1016/j.jcp.2019.108962

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)
https://doi.org/10.2166/hydro.2020.207

Nonlinear stability of two-layer shallow water flows with a free surface

Francisco de Melo Viríssimo and Paul A. Milewski
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2236) (2020)
https://doi.org/10.1098/rspa.2019.0594

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

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

Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model

Muhammad Rehan Saleem, Ubaid Ahmed Nisar and Shamsul Qamar
Advances in Mechanical Engineering 11 (9) 168781401987490 (2019)
https://doi.org/10.1177/1687814019874908

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)
https://doi.org/10.1051/m2an/2019044

Entropy-stable space–time DG schemes for non-conservative hyperbolic systems

Andreas Hiltebrand, Siddhartha Mishra and Carlos Parés
ESAIM: Mathematical Modelling and Numerical Analysis 52 (3) 995 (2018)
https://doi.org/10.1051/m2an/2017056

A two-layer model for the intrusion of two-phase debris flow into a river

Wei Liu and Siming He
Quarterly Journal of Engineering Geology and Hydrogeology 51 (1) 113 (2018)
https://doi.org/10.1144/qjegh2017-071

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

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

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

M. Rehan Saleem, Ishtiaq Ali and Shamsul Qamar
Results in Physics 8 379 (2018)
https://doi.org/10.1016/j.rinp.2017.12.044

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)
https://doi.org/10.1134/S0965542518050081

The immersed-body gas-solid interaction model for blast analysis in fractured solid media

P. Yang, J. Xiang, M. Chen, et al.
International Journal of Rock Mechanics and Mining Sciences 91 119 (2017)
https://doi.org/10.1016/j.ijrmms.2016.10.006

Global stability of weak solutions for a multilayer Saint–Venant model with interactions between layers

Bernard Di Martino, Boris Haspot and Yohan Penel
Nonlinear Analysis 163 177 (2017)
https://doi.org/10.1016/j.na.2017.07.010

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

Nino Krvavica, Ivica Kožar, Vanja Travaš and Nevenka Ožanić
Journal of Hydrology and Hydromechanics 65 (1) 49 (2017)
https://doi.org/10.1515/johh-2016-0039

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

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)
https://doi.org/10.1016/j.jcp.2017.04.018

Salt-Wedge Response to Variable River Flow and Sea-Level Rise in the Microtidal Rječina River Estuary, Croatia

Nino Krvavica, Vanja Travaš and Nevenka Ožanić
Journal of Coastal Research 33 (4) 802 (2017)
https://doi.org/10.2112/JCOASTRES-D-16-00053.1

Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

Abdelaziz Beljadid, Philippe G. LeFloch, Siddhartha Mishra and Carlos Parés
Communications in Computational Physics 21 (4) 913 (2017)
https://doi.org/10.4208/cicp.OA-2016-0019

Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models

L. Sarno, A. Carravetta, R. Martino, M.N. Papa and Y.-C. Tai
Advances in Water Resources 100 183 (2017)
https://doi.org/10.1016/j.advwatres.2016.12.014

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

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)
https://doi.org/10.20948/prepr-2016-69

A meshless method for numerical simulation of depth‐averaged turbulence flows using a k‐ϵ model

Yasser Alhuri, Fayssal Benkhaldoun, Driss Ouazar, Mohammed Seaid and Ahmed Taik
International Journal for Numerical Methods in Fluids 80 (1) 3 (2016)
https://doi.org/10.1002/fld.4067

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)
https://doi.org/10.1016/j.cam.2015.09.026

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)
https://doi.org/10.1016/j.crme.2015.05.002

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

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)
https://doi.org/10.4208/cicp.180513.230514a

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)
https://doi.org/10.1016/j.matcom.2013.04.016

A two-layer depth-averaged approach to describe the regime stratification in collapses of dry granular columns

L. Sarno, A. Carravetta, R. Martino and Y. C. Tai
Physics of Fluids 26 (10) (2014)
https://doi.org/10.1063/1.4898563

A positivity preserving central scheme for shallow water flows in channels with wet-dry states

Jorge Balbás and Gerardo Hernandez-Duenas
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 665 (2014)
https://doi.org/10.1051/m2an/2013106

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 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)
https://doi.org/10.1016/j.jcp.2014.04.026

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)
https://doi.org/10.1007/s12190-013-0703-z

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

Martin Parisot and Jean-Paul Vila
Comptes Rendus. Mathématique 352 (11) 953 (2014)
https://doi.org/10.1016/j.crma.2014.09.020

THREE-LAYER APPROXIMATION OF TWO-LAYER SHALLOW WATER EQUATIONS

Alina Chertock, Alexander Kurganov, Alexander Kurganov, Zhuolin Qu and Tong Wu
Mathematical Modelling and Analysis 18 (5) 675 (2013)
https://doi.org/10.3846/13926292.2013.869269

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)
https://doi.org/10.1051/m2an/2012036

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

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

Efficient well-balanced hydrostatic upwind schemes for shallow-water equations

Christophe Berthon and Françoise Foucher
Journal of Computational Physics 231 (15) 4993 (2012)
https://doi.org/10.1016/j.jcp.2012.02.031

A Shallow Water model for the numerical simulation of overland flow on surfaces with ridges and furrows

Ulrich Razafison, Stéphane Cordier, Olivier Delestre, et al.
European Journal of Mechanics - B/Fluids 31 44 (2012)
https://doi.org/10.1016/j.euromechflu.2011.07.002

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

A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods

M. J. Castro Díaz and E. Fernández-Nieto
SIAM Journal on Scientific Computing 34 (4) A2173 (2012)
https://doi.org/10.1137/100795280

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

Marica Pelanti, François Bouchut and Anne Mangeney
Journal of Computational Physics 230 (3) 515 (2011)
https://doi.org/10.1016/j.jcp.2010.10.001

Approximation of the hydrostatic Navier–Stokes system for density stratified flows by a multilayer model: Kinetic interpretation and numerical solution

E. Audusse, M.-O. Bristeau, M. Pelanti and J. Sainte-Marie
Journal of Computational Physics 230 (9) 3453 (2011)
https://doi.org/10.1016/j.jcp.2011.01.042

Multilayer Saint-Venant equations over movable beds

Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie and Mohammed Seaid
Discrete & Continuous Dynamical Systems - B 15 (4) 917 (2011)
https://doi.org/10.3934/dcdsb.2011.15.917

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)
https://doi.org/10.1016/j.advwatres.2011.05.002

Simplified two-layer models of precipitating atmosphere and their properties

J. Lambaerts, G. Lapeyre, V. Zeitlin and F. Bouchut
Physics of Fluids 23 (4) (2011)
https://doi.org/10.1063/1.3582356

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)
https://doi.org/10.1007/s10915-011-9465-7

A fast adaptive quadtree scheme for a two-layer shallow water model

Wei-Koon Lee, Alistair G.L. Borthwick and Paul H. Taylor
Journal of Computational Physics 230 (12) 4848 (2011)
https://doi.org/10.1016/j.jcp.2011.03.007

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)
https://doi.org/10.1051/m2an/2010036

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

Analyzing the tidal‐related origin of subinertial flows through the Strait of Gibraltar

M. Bruno, J. Macías, J. M. González‐Vida and A. Vázquez
Journal of Geophysical Research: Oceans 115 (C12) (2010)
https://doi.org/10.1029/2010JC006499

A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows

François Bouchut and Tomás Morales de Luna
SIAM Journal on Numerical Analysis 48 (5) 1733 (2010)
https://doi.org/10.1137/090758416

Two-Layer Shallow Water System: A Relaxation Approach

Rémi Abgrall and Smadar Karni
SIAM Journal on Scientific Computing 31 (3) 1603 (2009)
https://doi.org/10.1137/06067167X

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

A central scheme for shallow water flows along channels with irregular geometry

Jorge Balbás and Smadar Karni
ESAIM: Mathematical Modelling and Numerical Analysis 43 (2) 333 (2009)
https://doi.org/10.1051/m2an:2008050

First- and second-order finite volume methods for the one-dimensional nonconservative Euler system

Stéphane Clain and David Rochette
Journal of Computational Physics 228 (22) 8214 (2009)
https://doi.org/10.1016/j.jcp.2009.07.038

Central-Upwind Schemes for Two-Layer Shallow Water Equations

Alexander Kurganov and Guergana Petrova
SIAM Journal on Scientific Computing 31 (3) 1742 (2009)
https://doi.org/10.1137/080719091

Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods

M.J. Castro Díaz, E.D. Fernández-Nieto and A.M. Ferreiro
Computers & Fluids 37 (3) 299 (2008)
https://doi.org/10.1016/j.compfluid.2007.07.017

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