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:

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

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)
DOI: 10.1137/130908671
See this article

Computing Qualitatively Correct Approximations of Balance Laws

Laurent Gosse
SIMAI Springer Series, Computing Qualitatively Correct Approximations of Balance Laws 2 137 (2013)
DOI: 10.1007/978-88-470-2892-0_8
See this article

Dynamic simulation of a mountain disaster chain: landslides, barrier lakes, and outburst floods

Wei Liu and Siming He
Natural Hazards 90 (2) 757 (2018)
DOI: 10.1007/s11069-017-3073-2
See this article

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)
DOI: 10.1016/j.jcp.2006.06.015
See this article

Shallow Water Flows in Channels

Gerardo Hernández-Dueñas and Smadar Karni
Journal of Scientific Computing 48 (1-3) 190 (2011)
DOI: 10.1007/s10915-010-9430-x
See this article

Central-Upwind Schemes for the Saint-Venant System

Alexander Kurganov and Doron Levy
ESAIM: Mathematical Modelling and Numerical Analysis 36 (3) 397 (2002)
DOI: 10.1051/m2an:2002019
See this article

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)
DOI: 10.1016/j.jcp.2007.12.005
See this article

The generalized Riemann problem method for the shallow water equations with bottom topography

Jiequan Li and Guoxian Chen
International Journal for Numerical Methods in Engineering 65 (6) 834 (2006)
DOI: 10.1002/nme.1471
See this article

Solveurs simples positifs et entropiques pour les systèmes hyperboliques avec terme source

Gérard Gallice
Comptes Rendus Mathematique 334 (8) 713 (2002)
DOI: 10.1016/S1631-073X(02)02307-5
See this article

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)
DOI: 10.1007/s00574-016-0126-1
See this article

A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients

Gerardo Hernandez-Duenas
Journal of Scientific Computing 73 (2-3) 753 (2017)
DOI: 10.1007/s10915-017-0553-1
See this article

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)
DOI: 10.1007/s10915-015-0124-2
See this article

Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem

Matania Ben-Artzi and Jiequan Li
Numerische Mathematik 106 (3) 369 (2007)
DOI: 10.1007/s00211-007-0069-y
See this article

A steady state capturing and preserving method for computing hyperbolic systems with geometrical source terms having concentrations

Xin Wen
Journal of Computational Physics 219 (1) 322 (2006)
DOI: 10.1016/j.jcp.2006.03.019
See this article

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)
DOI: 10.1016/j.jcp.2011.03.042
See this article

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin
ESAIM: Mathematical Modelling and Numerical Analysis 37 (3) 479 (2003)
DOI: 10.1051/m2an:2003038
See this article

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)
DOI: 10.1137/060678373
See this article

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)
DOI: 10.1007/s10236-016-1001-8
See this article

FRONT TRACKING FOR SCALAR BALANCE EQUATIONS

K. H. KARLSEN, N. H. RISEBRO and J. D. TOWERS
Journal of Hyperbolic Differential Equations 01 (01) 115 (2004)
DOI: 10.1142/S0219891604000068
See this article

Mixed analytical/numerical method for flow equations with a source term

Tao Du, Jing Shi and Zi-Niu Wu
Computers & Fluids 32 (5) 659 (2003)
DOI: 10.1016/S0045-7930(02)00013-0
See this article

The space–time CE/SE method for solving single and two-phase shallow flow models

Shamsul Qamar, Saqib Zia and Waqas Ashraf
Computers & Fluids 96 136 (2014)
DOI: 10.1016/j.compfluid.2014.03.015
See this article

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)
DOI: 10.3934/nhm.2016.11.145
See this article

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)
DOI: 10.1002/fld.3736
See this article

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)
DOI: 10.1016/j.jcp.2009.05.028
See this article

A mass conservative scheme for simulating shallow flows over variable topographies using unstructured grid

A. Mohamadian, D.Y. Le Roux, M. Tajrishi and K. Mazaheri
Advances in Water Resources 28 (5) 523 (2005)
DOI: 10.1016/j.advwatres.2004.10.006
See this article

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)
DOI: 10.1007/s10915-012-9677-5
See this article

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)
DOI: 10.1080/10618562.2014.891019
See this article

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)
DOI: 10.1137/090758416
See this article

A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari and Fausto Saleri
ESAIM: Mathematical Modelling and Numerical Analysis 38 (2) 211 (2004)
DOI: 10.1051/m2an:2004010
See this article

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)
DOI: 10.1007/s10915-014-9908-z
See this article

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)
DOI: 10.4208/cicp.290615.060516a
See this article

A well-balanced positivity preserving “second-order” scheme for shallow water flows on unstructured meshes

Emmanuel Audusse and Marie-Odile Bristeau
Journal of Computational Physics 206 (1) 311 (2005)
DOI: 10.1016/j.jcp.2004.12.016
See this article

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)
DOI: 10.1137/100803067
See this article

High order finite difference WENO schemes with the exact conservation property for the shallow water equations

Yulong Xing and Chi-Wang Shu
Journal of Computational Physics 208 (1) 206 (2005)
DOI: 10.1016/j.jcp.2005.02.006
See this article

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)
DOI: 10.1051/m2an/2010060
See this article

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)
DOI: 10.1007/s00211-013-0597-6
See this article

Space Localization and Well-Balanced Schemes for Discrete Kinetic Models in Diffusive Regimes

Laurent Gosse and Giuseppe Toscani
SIAM Journal on Numerical Analysis 41 (2) 641 (2003)
DOI: 10.1137/S0036142901399392
See this article

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)
DOI: 10.1137/070686147
See this article

High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

Yulong Xing and Chi-Wang Shu
Journal of Computational Physics 214 (2) 567 (2006)
DOI: 10.1016/j.jcp.2005.10.005
See this article

Time asymptotic high order schemes for dissipative BGK hyperbolic systems

Denise Aregba-Driollet, Maya Briani and Roberto Natalini
Numerische Mathematik 132 (2) 399 (2016)
DOI: 10.1007/s00211-015-0720-y
See this article

Asymptotic preserving HLL schemes

Christophe Berthon and Rodolphe Turpault
Numerical Methods for Partial Differential Equations 27 (6) 1396 (2011)
DOI: 10.1002/num.20586
See this article

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)
DOI: 10.1016/S1574-6909(06)02004-1
See this article

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)
DOI: 10.1051/m2an:2008050
See this article

Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method

Emmanuel Audusse and Marie-Odile Bristeau
ESAIM: Mathematical Modelling and Numerical Analysis 37 (2) 389 (2003)
DOI: 10.1051/m2an:2003034
See this article

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)
DOI: 10.1007/s10915-016-0199-4
See this article

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)
DOI: 10.1016/j.jcp.2009.06.038
See this article

A Well-Balanced Gas-Kinetic Scheme for the Shallow-Water Equations with Source Terms

Kun Xu
Journal of Computational Physics 178 (2) 533 (2002)
DOI: 10.1006/jcph.2002.7040
See this article

High-order well-balanced central WENO scheme for pre-balanced shallow water equations

Gang Li, Valerio Caleffi and Jinmei Gao
Computers & Fluids 99 182 (2014)
DOI: 10.1016/j.compfluid.2014.04.022
See this article

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)
DOI: 10.1016/j.camwa.2016.05.015
See this article

Finite-volume schemes for shallow-water equations

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

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)
DOI: 10.1137/050635018
See this article

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)
DOI: 10.1007/s10915-015-0097-1
See this article

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)
DOI: 10.1016/j.cam.2017.10.027
See this article

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)
DOI: 10.1016/j.camwa.2006.02.055
See this article

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

Yulong Xing
Journal of Computational Physics 257 536 (2014)
DOI: 10.1016/j.jcp.2013.10.010
See this article

Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms

A. Duran and F. Marche
Computers & Fluids 101 88 (2014)
DOI: 10.1016/j.compfluid.2014.05.031
See this article

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)
DOI: 10.1007/s00211-017-0928-0
See this article

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

Jianzhen Qian, Jiequan Li and Shuanghu Wang
Journal of Computational Physics (2013)
DOI: 10.1016/j.jcp.2013.12.002
See this article

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)
DOI: 10.1007/s11069-016-2301-5
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

An efficient scheme on wet/dry transitions for shallow water equations with friction

Christophe Berthon, Fabien Marche and Rodolphe Turpault
Computers & Fluids 48 (1) 192 (2011)
DOI: 10.1016/j.compfluid.2011.04.011
See this article

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

Tomás Chacón Rebollo, Antonio Domı́nguez Delgado and Enrique D. Fernández Nieto
Comptes Rendus Mathematique 338 (1) 85 (2004)
DOI: 10.1016/j.crma.2003.11.008
See this article

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)
DOI: 10.1002/fld.3800
See this article

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

Christophe Berthon and Françoise Foucher
Journal of Computational Physics 231 (15) 4993 (2012)
DOI: 10.1016/j.jcp.2012.02.031
See this article

An entropy-correction free solver for non-homogeneous shallow water equations

Tomás Chacón Rebollo, Antonio Domínguez Delgado and Enrique D. Fernández Nieto
ESAIM: Mathematical Modelling and Numerical Analysis 37 (5) 755 (2003)
DOI: 10.1051/m2an:2003043
See this article

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

Sebastian Noelle, Normann Pankratz, Gabriella Puppo and Jostein R. Natvig
Journal of Computational Physics 213 (2) 474 (2006)
DOI: 10.1016/j.jcp.2005.08.019
See this article

WENO schemes for balance laws with spatially varying flux

Senka Vukovic, Nelida Crnjaric-Zic and Luka Sopta
Journal of Computational Physics 199 (1) 87 (2004)
DOI: 10.1016/j.jcp.2004.02.002
See this article

Upwind Schemes with Exact Conservation Property for One-Dimensional Open Channel Flow Equations

Senka Vukovic and Luka Sopta
SIAM Journal on Scientific Computing 24 (5) 1630 (2003)
DOI: 10.1137/S1064827501392211
See this article

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

Ramaz Botchorishvili and Olivier Pironneau
Journal of Computational Physics 187 (2) 391 (2003)
DOI: 10.1016/S0021-9991(03)00086-X
See this article

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)
DOI: 10.1016/j.jcp.2007.03.031
See this article

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)
DOI: 10.1016/j.jcp.2012.10.033
See this article

Upwinding sources at interfaces in conservation laws

Th Katsaounis, B Perthame and C Simeoni
Applied Mathematics Letters 17 (3) 309 (2004)
DOI: 10.1016/S0893-9659(04)90068-7
See this article

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

Xin Liu, Xi Chen, Shi Jin, et al.
SIAM Journal on Scientific Computing 42 (4) A2206 (2020)
DOI: 10.1137/19M1258098
See this article

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)
DOI: 10.1371/journal.pone.0197500
See this article

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)
DOI: 10.1016/j.jcp.2019.109137
See this article

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)
DOI: 10.1007/978-3-319-91545-6_28
See this article

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)
DOI: 10.3934/nhm.2016.11.69
See this article

Two Interface-Type Numerical Methods for Computing Hyperbolic Systems with Geometrical Source Terms Having Concentrations

Shi Jin and Xin Wen
SIAM Journal on Scientific Computing 26 (6) 2079 (2005)
DOI: 10.1137/040605825
See this article

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)
DOI: 10.1016/j.amc.2015.04.054
See this article

TWO MOMENT SYSTEMS FOR COMPUTING MULTIPHASE SEMICLASSICAL LIMITS OF THE SCHRÖDINGER EQUATION

LAURENT GOSSE, SHI JIN and XIANTAO LI
Mathematical Models and Methods in Applied Sciences 13 (12) 1689 (2003)
DOI: 10.1142/S0218202503003082
See this article

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)
DOI: 10.1142/S0578563415500175
See this article

From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks

F. Berthelin and A. Vasseur
SIAM Journal on Mathematical Analysis 36 (6) 1807 (2005)
DOI: 10.1137/S0036141003431554
See this article

A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows

Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau, Rupert Klein and Benoı⁁t Perthame
SIAM Journal on Scientific Computing 25 (6) 2050 (2004)
DOI: 10.1137/S1064827503431090
See this article

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)
DOI: 10.1016/j.matcom.2016.12.012
See this article

Improved non-staggered central NT schemes for balance laws with geometrical source terms

N. ?rnjari?-?ic, S. Vukovi? and L. Sopta
International Journal for Numerical Methods in Fluids 46 (8) 849 (2004)
DOI: 10.1002/fld.790
See this article

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)
DOI: 10.1016/j.jcp.2015.02.007
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

Stochastic Galerkin Finite Volume Shallow Flow Model: Well-Balanced Treatment over Uncertain Topography

James Shaw and Georges Kesserwani
Journal of Hydraulic Engineering 146 (3) 04020005 (2020)
DOI: 10.1061/(ASCE)HY.1943-7900.0001705
See this article

A Two-Dimensional Numerical Model for Shallow Water Flows over Variable Topographies

Biao Lv and Shao Xi Li
Applied Mechanics and Materials 580-583 1793 (2014)
DOI: 10.4028/www.scientific.net/AMM.580-583.1793
See this article

Relaxation schemes for the shallow water equations

A. I. Delis and Th. Katsaounis
International Journal for Numerical Methods in Fluids 41 (7) 695 (2003)
DOI: 10.1002/fld.462
See this article

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)
DOI: 10.1016/j.camwa.2018.12.019
See this article

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)
DOI: 10.1007/s10092-006-0123-7
See this article

Hyperbolic Problems: Theory, Numerics, Applications

Theodoros Katsaounis and Charalambos Makridakis
Hyperbolic Problems: Theory, Numerics, Applications 621 (2003)
DOI: 10.1007/978-3-642-55711-8_58
See this article

Proceedings of the Conference on Applied Mathematics and Scientific Computing

Senka Vuković, Nelida Črnjarić-Žic and Luka Sopta
Proceedings of the Conference on Applied Mathematics and Scientific Computing 329 (2005)
DOI: 10.1007/1-4020-3197-1_25
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

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) 04015012 (2015)
DOI: 10.1061/(ASCE)HE.1943-5584.0001171
See this article

Trends and Applications of Mathematics to Mechanics

Giovanni Russo
Trends and Applications of Mathematics to Mechanics 225 (2005)
DOI: 10.1007/88-470-0354-7_18
See this article

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)
DOI: 10.1016/j.camwa.2017.10.021
See this article

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)
DOI: 10.1016/j.jcp.2017.01.009
See this article

Hyperbolic Problems: Theory, Numerics, Applications

M. Kraft and M. Lukáčcová-Medviďová
Hyperbolic Problems: Theory, Numerics, Applications 695 (2008)
DOI: 10.1007/978-3-540-75712-2_70
See this article

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)
DOI: 10.1002/fld.1167
See this article

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)
DOI: 10.1007/978-3-642-20671-9_11
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

A central-upwind scheme with artificial viscosity for shallow-water flows in channels

Gerardo Hernandez-Duenas and Abdelaziz Beljadid
Advances in Water Resources 96 323 (2016)
DOI: 10.1016/j.advwatres.2016.07.021
See this article

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)
DOI: 10.1007/978-3-642-33221-0_8
See this article

Edwige Godlewski and Pierre-Arnaud Raviart
118 627 (2021)
DOI: 10.1007/978-1-0716-1344-3_7
See this article

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)
DOI: 10.1016/j.apnum.2020.11.019
See this article

An effect non-staggered central scheme based on new hydrostatic reconstruction

Jian Dong and Ding Fang Li
Applied Mathematics and Computation 372 124992 (2020)
DOI: 10.1016/j.amc.2019.124992
See this article

Energy-stable staggered schemes for the Shallow Water equations

Arnaud Duran, Jean-Paul Vila and Rémy Baraille
Journal of Computational Physics 401 109051 (2020)
DOI: 10.1016/j.jcp.2019.109051
See this article

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)
DOI: 10.1177/16878140211045240
See this article

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)
DOI: 10.1002/mma.6597
See this article

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)
DOI: 10.1016/j.jcp.2017.12.026
See this article

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)
DOI: 10.1016/j.jcp.2018.07.038
See this article

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)
DOI: 10.3390/math9101079
See this article

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)
DOI: 10.1002/fld.4506
See this article

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)
DOI: 10.1137/19M1284476
See this article

Luka Sopta, Nelida Črnjarić-Žic, Senka Vuković, Danko Holjević, Jerko Škifić and Siniša Družeta
293 (2005)
DOI: 10.1007/1-4020-3197-1_22
See this article

Benoît Perthame and Chiara Simeoni
61 (2003)
DOI: 10.1007/978-3-642-55711-8_5
See this article

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)
DOI: 10.1016/j.apples.2021.100048
See this article