EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 35 4 (2001) 631-645 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

Modeling Phase Separation in Grain‐Fluid Mixture Flows by a Depth‐Averaged Approach With Dilatancy Effects

Weihang Sun and Yongqi Wang
Journal of Geophysical Research: Earth Surface 129 (12) (2024)
https://doi.org/10.1029/2023JF007416

Andrea Gilberto Filippini, Luca Arpaia, Vincent Perrier, Rodrigo Pedreros, Philippe Bonneton, David Lannes, Fabien Marche, Sebastien De Brye, Simon Delmas, Sophie Lecacheux, Faiza Boulahya and Mario Ricchiuto
(2024)
https://doi.org/10.2139/ssrn.4808242

A positivity-preserving well-balanced wet-dry front reconstruction for shallow water equations on rectangular grids

Xue Wang and Guoxian Chen
Applied Numerical Mathematics 198 295 (2024)
https://doi.org/10.1016/j.apnum.2024.01.012

An operational discontinuous Galerkin shallow water model for coastal flood assessment

A.G. Filippini, L. Arpaia, V. Perrier, R. Pedreros, P. Bonneton, D. Lannes, F. Marche, S. De Brye, S. Delmas, S. Lecacheux, F. Boulahya and M. Ricchiuto
Ocean Modelling 192 102447 (2024)
https://doi.org/10.1016/j.ocemod.2024.102447

Semi-discrete entropy-preserving surface reconstruction schemes for the shallow water equations: Analysis of physical structures

Jian Dong and Xu Qian
Journal of Computational Physics 508 112995 (2024)
https://doi.org/10.1016/j.jcp.2024.112995

A Well-Balanced Scheme for Euler Equations with Singular Sources

Changsheng Yu, T. G. Liu and Chengliang Feng
SIAM Journal on Scientific Computing 45 (4) A2119 (2023)
https://doi.org/10.1137/22M1473224

A central-upwind scheme for two-phase shallow granular flow model

Hossam A. Nabwey, Shahid Mehmood, Saqib Zia, Asad Rehman, Muhammad Ashraf and A.M. Rashad
Alexandria Engineering Journal 82 291 (2023)
https://doi.org/10.1016/j.aej.2023.09.079

Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws

I. Gómez-Bueno, S. Boscarino, M.J. Castro, C. Parés and G. Russo
Applied Numerical Mathematics 184 18 (2023)
https://doi.org/10.1016/j.apnum.2022.09.016

A unified surface-gradient and hydrostatic reconstruction scheme for the shallow water equations

Guoxian Chen and Sebastian Noelle
Journal of Computational Physics 467 111463 (2022)
https://doi.org/10.1016/j.jcp.2022.111463

High-Order Godunov-Type Scheme for Conservation Laws with Discontinuous Flux Function in Space

Qianqian Wei, Guodong Wang and Yanying Ma
International Journal of Computational Methods 19 (03) (2022)
https://doi.org/10.1142/S0219876221500663

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

Numerical solution of compressible Euler and Magnetohydrodynamic flow past an infinite cone

Ian Holloway and Sivaguru S. Sritharan
Applications in Engineering Science 6 100048 (2021)
https://doi.org/10.1016/j.apples.2021.100048

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) (2021)
https://doi.org/10.1177/16878140211045240

High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space

Tingting Xiang, Guodong Wang and Suping Zhang
Mathematics 9 (10) 1079 (2021)
https://doi.org/10.3390/math9101079

A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography

Jian Dong and Ding Fang Li
Applied Numerical Mathematics 161 408 (2021)
https://doi.org/10.1016/j.apnum.2020.11.019

A Direct Eulerian GRP Scheme for a Blood Flow Model in Arteries

Wancheng Sheng, Qinglong Zhang and Yuxi Zheng
SIAM Journal on Scientific Computing 43 (3) A1975 (2021)
https://doi.org/10.1137/19M1284476

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)
https://doi.org/10.1002/fld.4887

Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System

Xin Liu, Xi Chen, Shi Jin, Alexander Kurganov, Tong Wu and Hui Yu
SIAM Journal on Scientific Computing 42 (4) A2206 (2020)
https://doi.org/10.1137/19M1258098

A robust central scheme for the shallow water flows with an abrupt topography based on modified hydrostatic reconstructions

Jian Dong
Mathematical Methods in the Applied Sciences 43 (15) 9024 (2020)
https://doi.org/10.1002/mma.6597

Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes

F.E. Uilhoorn
Journal of Computational Physics 404 109137 (2020)
https://doi.org/10.1016/j.jcp.2019.109137

Energy-stable staggered schemes for the Shallow Water equations

Arnaud Duran, Jean-Paul Vila and Rémy Baraille
Journal of Computational Physics 401 109051 (2020)
https://doi.org/10.1016/j.jcp.2019.109051

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)
https://doi.org/10.1007/s10915-019-00961-y

A fast, robust, and simple Lagrangian–Eulerian solver for balance laws and applications

Eduardo Abreu and John Pérez
Computers & Mathematics with Applications 77 (9) 2310 (2019)
https://doi.org/10.1016/j.camwa.2018.12.019

A high‐order PIC method for advection‐dominated flow with application to shallow water waves

W. Wang and D.M. Kelly
International Journal for Numerical Methods in Fluids 87 (11) 583 (2018)
https://doi.org/10.1002/fld.4506

High order well-balanced discontinuous Galerkin methods based on hydrostatic reconstruction for shallow water equations

Gang Li, Lina Song and Jinmei Gao
Journal of Computational and Applied Mathematics 340 546 (2018)
https://doi.org/10.1016/j.cam.2017.10.027

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

M. Rehan Saleem, Waqas Ashraf, Saqib Zia, et al.
PLOS ONE 13 (5) e0197500 (2018)
https://doi.org/10.1371/journal.pone.0197500

Well-balanced schemes for the shallow water equations with Coriolis forces

Alina Chertock, Michael Dudzinski, Alexander Kurganov and Mária Lukáčová-Medvid’ová
Numerische Mathematik 138 (4) 939 (2018)
https://doi.org/10.1007/s00211-017-0928-0

Well-balanced positivity preserving central-upwind scheme with a novel wet/dry reconstruction on triangular grids for the Saint-Venant system

Xin Liu, Jason Albright, Yekaterina Epshteyn and Alexander Kurganov
Journal of Computational Physics 374 213 (2018)
https://doi.org/10.1016/j.jcp.2018.07.038

The space–time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

M. Rehan Saleem, Saqib Zia, Waqas Ashraf, Ishtiaq Ali and Shamsul Qamar
Computers & Mathematics with Applications 75 (3) 933 (2018)
https://doi.org/10.1016/j.camwa.2017.10.021

Theory, Numerics and Applications of Hyperbolic Problems I

Alina Chertock, Michael Herty and Şeyma Nur Özcan
Springer Proceedings in Mathematics & Statistics, Theory, Numerics and Applications of Hyperbolic Problems I 236 345 (2018)
https://doi.org/10.1007/978-3-319-91545-6_28

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

Alina Chertock, Shumo Cui, Alexander Kurganov, Şeyma Nur Özcan and Eitan Tadmor
Journal of Computational Physics 358 36 (2018)
https://doi.org/10.1016/j.jcp.2017.12.026

A new finite volume approach for transport models and related applications with balancing source terms

E. Abreu, W. Lambert, J. Perez and A. Santo
Mathematics and Computers in Simulation 137 2 (2017)
https://doi.org/10.1016/j.matcom.2016.12.012

A well-balanced scheme for the shallow-water equations with topography or Manning friction

Victor Michel-Dansac, Christophe Berthon, Stéphane Clain and Françoise Foucher
Journal of Computational Physics 335 115 (2017)
https://doi.org/10.1016/j.jcp.2017.01.009

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)
https://doi.org/10.1016/bs.hna.2016.09.003

A well-balanced scheme for the shallow-water equations with topography

Victor Michel-Dansac, Christophe Berthon, Stéphane Clain and Françoise Foucher
Computers & Mathematics with Applications 72 (3) 568 (2016)
https://doi.org/10.1016/j.camwa.2016.05.015

Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls

Adimurthi, Aekta Aggarwal and G. D. Veerappa Gowda
Communications in Computational Physics 20 (4) 1071 (2016)
https://doi.org/10.4208/cicp.290615.060516a

A shallow water with variable pressure model for blood flow simulation

Pierre-Yves Lagrée, José-Maria Fullana, Arthur R. Ghigo and Olivier Delestre
Networks and Heterogeneous Media 11 (1) 69 (2016)
https://doi.org/10.3934/nhm.2016.11.69

Time asymptotic high order schemes for dissipative BGK hyperbolic systems

Denise Aregba-Driollet, Maya Briani and Roberto Natalini
Numerische Mathematik 132 (2) 399 (2016)
https://doi.org/10.1007/s00211-015-0720-y

Validation of the FAST forecast model for the storm surges due to hurricanes Wilma and Ike

David M. Kelly, Yi-Cheng Teng, Yuepeng Li and Keqi Zhang
Natural Hazards 83 (1) 53 (2016)
https://doi.org/10.1007/s11069-016-2301-5

Finite Volume Scheme with Local High Order Discretization of the Hydrostatic Equilibrium for the Euler Equations with External Forces

Emmanuel Franck and Laura S. Mendoza
Journal of Scientific Computing 69 (1) 314 (2016)
https://doi.org/10.1007/s10915-016-0199-4

A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs

Shi Jin, Dongbin Xiu and Xueyu Zhu
Journal of Scientific Computing 67 (3) 1198 (2016)
https://doi.org/10.1007/s10915-015-0124-2

Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations

C. Berthon, C. Chalons, S. Cornet and G. Sperone
Bulletin of the Brazilian Mathematical Society, New Series 47 (1) 117 (2016)
https://doi.org/10.1007/s00574-016-0126-1

Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography

Siddhartha Mishra and Andreas Hiltebrand
Networks and Heterogeneous Media 11 (1) 145 (2016)
https://doi.org/10.3934/nhm.2016.11.145

A Well-Balanced Finite Volume Scheme for a Mixed Hyperbolic/Parabolic System to Model Chemotaxis

Christophe Berthon, Anaïs Crestetto and Françoise Foucher
Journal of Scientific Computing 67 (2) 618 (2016)
https://doi.org/10.1007/s10915-015-0097-1

A numerical study of the impact of hurricane-induced storm surge on the Herbert Hoover Dike at Lake Okeechobee, Florida

Yuepeng Li, Yi-Cheng Teng, David M. Kelly and Keqi Zhang
Ocean Dynamics 66 (12) 1699 (2016)
https://doi.org/10.1007/s10236-016-1001-8

Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System

Suo Yang, Alexander Kurganov and Yingjie Liu
Journal of Scientific Computing 63 (3) 678 (2015)
https://doi.org/10.1007/s10915-014-9908-z

A well-balanced finite difference WENO scheme for shallow water flow model

Gang Li, Valerio Caleffi and Zhengkun Qi
Applied Mathematics and Computation 265 1 (2015)
https://doi.org/10.1016/j.amc.2015.04.054

A Numerical Model for Storm Surges that Involve the Inundation of Complex Landscapes

David M. Kelly, Yi-Cheng Teng, Yuepeng Li and Keqi Zhang
Coastal Engineering Journal 57 (4) 1550017-1 (2015)
https://doi.org/10.1142/S0578563415500175

Overland Flow Modeling with the Shallow Water Equations Using a Well-Balanced Numerical Scheme: Better Predictions or Just More Complexity

M. Rousseau, O. Cerdan, O. Delestre, et al.
Journal of Hydrologic Engineering 20 (10) (2015)
https://doi.org/10.1061/(ASCE)HE.1943-5584.0001171

Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes

A. Duran, F. Marche, R. Turpault and C. Berthon
Journal of Computational Physics 287 184 (2015)
https://doi.org/10.1016/j.jcp.2015.02.007

Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium

Yulong Xing
Journal of Computational Physics 257 536 (2014)
https://doi.org/10.1016/j.jcp.2013.10.010

Numerical solution of shallow water magnetohydrodynamic equations with non-flat bottom topography

Saqib Zia, Munshoor Ahmed and Shamsul Qamar
International Journal of Computational Fluid Dynamics 28 (1-2) 56 (2014)
https://doi.org/10.1080/10618562.2014.891019

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)
https://doi.org/10.4208/cicp.060712.210313a

Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

Alina Chertock, Alexander Kurganov and Yu Liu
Numerische Mathematik 127 (4) 595 (2014)
https://doi.org/10.1007/s00211-013-0597-6

Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Yunlong Chen, Alexander Kurganov, Minlan Lei and Yu Liu
Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws 120 125 (2013)
https://doi.org/10.1007/978-3-642-33221-0_8

A ‘well‐balanced’ finite volume scheme for blood flow simulation

O. Delestre and P.‐Y. Lagrée
International Journal for Numerical Methods in Fluids 72 (2) 177 (2013)
https://doi.org/10.1002/fld.3736

Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

Christophe Chalons, Mathieu Girardin and Samuel Kokh
SIAM Journal on Scientific Computing 35 (6) A2874 (2013)
https://doi.org/10.1137/130908671

A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations

Andreas Bollermann, Guoxian Chen, Alexander Kurganov and Sebastian Noelle
Journal of Scientific Computing 56 (2) 267 (2013)
https://doi.org/10.1007/s10915-012-9677-5

On the well-balanced numerical discretization of shallow water equations on unstructured meshes

A. Duran, Q. Liang and F. Marche
Journal of Computational Physics 235 565 (2013)
https://doi.org/10.1016/j.jcp.2012.10.033

The generalized Riemann problems for compressible fluid flows: Towards high order

Jianzhen Qian, Jiequan Li and Shuanghu Wang
Journal of Computational Physics (2013)
https://doi.org/10.1016/j.jcp.2013.12.002

Computing Qualitatively Correct Approximations of Balance Laws

Laurent Gosse
SIMAI Springer Series, Computing Qualitatively Correct Approximations of Balance Laws 2 137 (2013)
https://doi.org/10.1007/978-88-470-2892-0_8

A well‐balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes

Feng Zhou, Guoxian Chen, Sebastian Noelle and Huaicheng Guo
International Journal for Numerical Methods in Fluids 73 (3) 266 (2013)
https://doi.org/10.1002/fld.3800

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

Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis

R. Natalini and M. Ribot
SIAM Journal on Numerical Analysis 50 (2) 883 (2012)
https://doi.org/10.1137/100803067

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov and Guergana Petrova
ESAIM: Mathematical Modelling and Numerical Analysis 45 (3) 423 (2011)
https://doi.org/10.1051/m2an/2010060

Finite Volumes for Complex Applications VI Problems & Perspectives

Christophe Berthon and Françoise Foucher
Springer Proceedings in Mathematics, Finite Volumes for Complex Applications VI Problems & Perspectives 4 97 (2011)
https://doi.org/10.1007/978-3-642-20671-9_11

Asymptotic preserving HLL schemes

Christophe Berthon and Rodolphe Turpault
Numerical Methods for Partial Differential Equations 27 (6) 1396 (2011)
https://doi.org/10.1002/num.20586

Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

Ulrik S. Fjordholm, Siddhartha Mishra and Eitan Tadmor
Journal of Computational Physics 230 (14) 5587 (2011)
https://doi.org/10.1016/j.jcp.2011.03.042

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

High-order well-balanced schemes and applications to non-equilibrium flow

Wei Wang, Chi-Wang Shu, H.C. Yee and Björn Sjögreen
Journal of Computational Physics 228 (18) 6682 (2009)
https://doi.org/10.1016/j.jcp.2009.05.028

A Finite Variable Difference Relaxation Scheme for hyperbolic–parabolic equations

Mayank Bajpayi and S.V. Raghurama Rao
Journal of Computational Physics 228 (20) 7513 (2009)
https://doi.org/10.1016/j.jcp.2009.06.038

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

A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations: A Class of Relaxation Schemes

Christophe Berthon and Fabien Marche
SIAM Journal on Scientific Computing 30 (5) 2587 (2008)
https://doi.org/10.1137/070686147

Asymptotic High-Order Schemes for $2\times2$ Dissipative Hyperbolic Systems

Denise Aregba-Driollet, Maya Briani and Roberto Natalini
SIAM Journal on Numerical Analysis 46 (2) 869 (2008)
https://doi.org/10.1137/060678373

Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

Michael Dumbser, Cedric Enaux and Eleuterio F. Toro
Journal of Computational Physics 227 (8) 3971 (2008)
https://doi.org/10.1016/j.jcp.2007.12.005

Well-balanced finite volume evolution Galerkin methods for the shallow water equations

M. Lukáčová-Medvid’ová, S. Noelle and M. Kraft
Journal of Computational Physics 221 (1) 122 (2007)
https://doi.org/10.1016/j.jcp.2006.06.015

High-order well-balanced finite volume WENO schemes for shallow water equation with moving water

Sebastian Noelle, Yulong Xing and Chi-Wang Shu
Journal of Computational Physics 226 (1) 29 (2007)
https://doi.org/10.1016/j.jcp.2007.03.031

Upwinding of the source term at interfaces for Euler equations with high friction

Francois Bouchut, Haythem Ounaissa and Benoît Perthame
Computers & Mathematics with Applications 53 (3-4) 361 (2007)
https://doi.org/10.1016/j.camwa.2006.02.055

Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

François Bouchut
Edited Series on Advances in Nonlinear Science and Complexity, Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2 189 (2007)
https://doi.org/10.1016/S1574-6909(06)02004-1

Well-balanced schemes versus fractional step method for hyperbolic systems with source terms

Thierry Gallouet, Jean-Marc Hérard, Olivier Hurisse and Alain-Yves LeRoux
Calcolo 43 (4) 217 (2006)
https://doi.org/10.1007/s10092-006-0123-7

High‐Resolution Finite Volume Methods for Dusty Gas Jets and Plumes

Marica Pelanti and Randall J. LeVeque
SIAM Journal on Scientific Computing 28 (4) 1335 (2006)
https://doi.org/10.1137/050635018

Simulation of shallow flows over variable topographies using unstructured grids

A. Mohammadian and D. Y. Le Roux
International Journal for Numerical Methods in Fluids 52 (5) 473 (2006)
https://doi.org/10.1002/fld.1167