EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 36 3 (2002) 397-425 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):

r − adaptation for Shallow Water flows: conservation, well balancedness, efficiency

Luca Arpaia and Mario Ricchiuto
Computers & Fluids 160 175 (2018)
DOI: 10.1016/j.compfluid.2017.10.026
See this article

Modeling the sandpit dynamics in river flows

Iryna Gorban
Hydrodynamics and acoustics 1 (2) 132 (2018)
DOI: 10.15407/jha2018.02.132
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

A new finite volume method for flux-gradient and source-term balancing in shallow water equations

Fayssal Benkhaldoun, Imad Elmahi and Mohammed Seaïd
Computer Methods in Applied Mechanics and Engineering 199 (49-52) 3324 (2010)
DOI: 10.1016/j.cma.2010.07.003
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

Boundary value problems for the shallow water equations with topography

Ming-Cheng Shiue, Jacques Laminie, Roger Temam and Joseph Tribbia
Journal of Geophysical Research 116 (C2) C02015 (2011)
DOI: 10.1029/2010JC006315
See this article

A higher-order macroscopic model for pedestrian flows

Yan-qun Jiang, Peng Zhang, S.C. Wong and Ru-xun Liu
Physica A: Statistical Mechanics and its Applications 389 (21) 4623 (2010)
DOI: 10.1016/j.physa.2010.05.003
See this article

Central schemes on overlapping cells

Yingjie Liu
Journal of Computational Physics 209 (1) 82 (2005)
DOI: 10.1016/j.jcp.2005.03.014
See this article

Modeling of Breaching Due to Overtopping Flow and Waves Based on Coupled Flow and Sediment Transport

Zhiguo He, Peng Hu, Liang Zhao, Gangfeng Wu and Thomas Pähtz
Water 7 (8) 4283 (2015)
DOI: 10.3390/w7084283
See this article

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)
DOI: 10.1051/m2an/2013106
See this article

Advances in Hydroinformatics

Geoffroy Kirstetter, François Bourgin, Pierre Brigode and Olivier Delestre
Springer Water, Advances in Hydroinformatics 335 (2020)
DOI: 10.1007/978-981-15-5436-0_25
See this article

Encyclopedia of Computational Mechanics Second Edition

Thierry Dubois, Francois Jauberteau and Roger M. Temam
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm2059
See this article

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

Yulong Xing and Xiangxiong Zhang
Journal of Scientific Computing 57 (1) 19 (2013)
DOI: 10.1007/s10915-013-9695-y
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

Finite-volume schemes for shallow-water equations

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

Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms

A. Chertock, S. Cui, A. Kurganov and T. Wu
International Journal for Numerical Methods in Fluids 78 (6) 355 (2015)
DOI: 10.1002/fld.4023
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

Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes

Fayssal Benkhaldoun, Imad Elmahi and Mohammed Seaı¨d
Journal of Computational Physics 226 (1) 180 (2007)
DOI: 10.1016/j.jcp.2007.04.005
See this article

On a hybrid finite-volume-particle method

Alina Chertock and Alexander Kurganov
ESAIM: Mathematical Modelling and Numerical Analysis 38 (6) 1071 (2004)
DOI: 10.1051/m2an:2004051
See this article

High-order finite volume WENO schemes for the shallow water equations with dry states

Yulong Xing and Chi-Wang Shu
Advances in Water Resources 34 (8) 1026 (2011)
DOI: 10.1016/j.advwatres.2011.05.008
See this article

Numerical resolution of well-balanced shallow water equations with complex source terms

Qiuhua Liang and Fabien Marche
Advances in Water Resources 32 (6) 873 (2009)
DOI: 10.1016/j.advwatres.2009.02.010
See this article

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)
DOI: 10.1016/j.compfluid.2007.07.017
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

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

A robust and well-balanced scheme for the 2D Saint-Venant system on unstructured meshes with friction source term

A. Duran
International Journal for Numerical Methods in Fluids 78 (2) 89 (2015)
DOI: 10.1002/fld.4011
See this article

Simulation and visualization of the Saint-Venant system using GPUs

André R. Brodtkorb, Trond R. Hagen, Knut-Andreas Lie and Jostein R. Natvig
Computing and Visualization in Science 13 (7) 341 (2010)
DOI: 10.1007/s00791-010-0149-x
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

CWENO-type central-upwind schemes for multidimensional Saint-Venant system of shallow water equations

Jian-Hu Feng, Li Cai and Wen-Xian Xie
Applied Numerical Mathematics 56 (7) 1001 (2006)
DOI: 10.1016/j.apnum.2005.09.002
See this article

Space–time discontinuous Galerkin discretization of rotating shallow water equations

V.R. Ambati and O. Bokhove
Journal of Computational Physics 225 (2) 1233 (2007)
DOI: 10.1016/j.jcp.2007.01.036
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 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

A two-dimensional numerical scheme of dry/wet fronts for the Saint-Venant system of shallow water equations

Zsolt Horváth, Jürgen Waser, Rui A. P. Perdigão, Artem Konev and Günter Blöschl
International Journal for Numerical Methods in Fluids 77 (3) 159 (2015)
DOI: 10.1002/fld.3983
See this article

Computations of shallow water equations with high-order central-upwind schemes on triangular meshes

Wen-Xian Xie, Li Cai, Jian-Hu Feng and Wei Xu
Applied Mathematics and Computation 170 (1) 296 (2005)
DOI: 10.1016/j.amc.2004.11.027
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

Augmented Riemann solver for urethra flow modeling

Marek Brandner, Jiří Egermaier and Hana Kopincová
Mathematics and Computers in Simulation 80 (6) 1222 (2010)
DOI: 10.1016/j.matcom.2009.08.009
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

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

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

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

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

Randall J. LeVeque
Journal of Scientific Computing 48 (1-3) 209 (2011)
DOI: 10.1007/s10915-010-9411-0
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 sign matrix based scheme for non-homogeneous PDE’s with an analysis of the convergence stagnation phenomenon

Slah Sahmim, Fayssal Benkhaldoun and Francisco Alcrudo
Journal of Computational Physics 226 (2) 1753 (2007)
DOI: 10.1016/j.jcp.2007.06.017
See this article

Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Yulong Xing, Xiangxiong Zhang and Chi-Wang Shu
Advances in Water Resources 33 (12) 1476 (2010)
DOI: 10.1016/j.advwatres.2010.08.005
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

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

Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations

Nelida Črnjarić-Žic, Senka Vuković and Luka Sopta
Journal of Computational Physics 200 (2) 512 (2004)
DOI: 10.1016/j.jcp.2004.04.012
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

Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues

A. Kurganov
Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues 17 525 (2016)
DOI: 10.1016/bs.hna.2016.09.008
See this article

Development of a Cell-Centered Godunov-Type Finite Volume Model for Shallow Water Flow Based on Unstructured Mesh

Gangfeng Wu, Zhiguo He and Guohua Liu
Mathematical Problems in Engineering 2014 1 (2014)
DOI: 10.1155/2014/257915
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

Compressible two-phase flows by central and upwind schemes

Smadar Karni, Eduard Kirr, Alexander Kurganov and Guergana Petrova
ESAIM: Mathematical Modelling and Numerical Analysis 38 (3) 477 (2004)
DOI: 10.1051/m2an:2004024
See this article

Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term

Alina Chertock, Shumo Cui, Alexander Kurganov and Tong Wu
SIAM Journal on Numerical Analysis 53 (4) 2008 (2015)
DOI: 10.1137/151005798
See this article

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

Steve Bryson and Doron Levy
SIAM Journal on Scientific Computing 27 (2) 532 (2005)
DOI: 10.1137/040605539
See this article

A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations

Maojun Li, Philippe Guyenne, Fengyan Li and Liwei Xu
Journal of Scientific Computing 71 (3) 994 (2017)
DOI: 10.1007/s10915-016-0329-z
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

Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling

Muhammad Akbar and Shahrouz Aliabadi
Environmental Modelling & Software 46 118 (2013)
DOI: 10.1016/j.envsoft.2013.03.003
See this article

A higher order Finite Volume resolution method for a system related to the inviscid primitive equations in a complex domain

Arthur Bousquet, Gung-Min Gie, Youngjoon Hong and Jacques Laminie
Numerische Mathematik 128 (3) 431 (2014)
DOI: 10.1007/s00211-014-0622-4
See this article

Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation

David L. George
Journal of Computational Physics 227 (6) 3089 (2008)
DOI: 10.1016/j.jcp.2007.10.027
See this article

Computations of transport of pollutant in shallow water

Li Cai, Wen-Xian Xie, Jian-Hu Feng and Jun Zhou
Applied Mathematical Modelling 31 (3) 490 (2007)
DOI: 10.1016/j.apm.2005.11.011
See this article

A multilevel method for finite volume discretization of the two-dimensional nonlinear shallow-water equations

K. Adamy, A. Bousquet, S. Faure, J. Laminie and R. Temam
Ocean Modelling 33 (3-4) 235 (2010)
DOI: 10.1016/j.ocemod.2010.02.006
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

A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

Sheng Bi, Jianzhong Zhou, Yi Liu and Lixiang Song
Mathematical Problems in Engineering 2014 1 (2014)
DOI: 10.1155/2014/209562
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

High-Order Well-Balanced Finite Difference WENO Schemes for a Class of Hyperbolic Systems with Source Terms

Yulong Xing and Chi-Wang Shu
Journal of Scientific Computing 27 (1-3) 477 (2006)
DOI: 10.1007/s10915-005-9027-y
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

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

A kinetic scheme for the one-dimensional open channel flow equations with applications on networks

Arne Roggensack
Calcolo 50 (4) 255 (2013)
DOI: 10.1007/s10092-012-0066-0
See this article

Open Water Flow in a Wet/Dry Multiply-Connected Channel Network: A Robust Numerical Modeling Algorithm

Sergii Kivva, Mark Zheleznyak, Oleksandr Pylypenko and Vasyl Yoschenko
Pure and Applied Geophysics 177 (7) 3421 (2020)
DOI: 10.1007/s00024-020-02416-0
See this article

Spatial structure of shock formation

J. Eggers, T. Grava, M. A. Herrada and G. Pitton
Journal of Fluid Mechanics 820 208 (2017)
DOI: 10.1017/jfm.2017.205
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

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

Advances in Hydroinformatics

Bobby Minola Ginting and Ralf-Peter Mundani
Springer Water, Advances in Hydroinformatics 51 (2018)
DOI: 10.1007/978-981-10-7218-5_4
See this article

Higher Order Finite Volume Central Schemes for Multi-dimensional Hyperbolic Problems

Prabal Singh Verma and Wolf-Christian Müller
Journal of Scientific Computing 75 (2) 941 (2018)
DOI: 10.1007/s10915-017-0567-8
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

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

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

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

Visual simulation of shallow-water waves

T.R. Hagen, J.M. Hjelmervik, K.-A. Lie, J.R. Natvig and M. Ofstad Henriksen
Simulation Modelling Practice and Theory 13 (8) 716 (2005)
DOI: 10.1016/j.simpat.2005.08.006
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

Central unstaggered finite volume schemes for hyperbolic systems: Applications to unsteady shallow water equations

R. Touma
Applied Mathematics and Computation 213 (1) 47 (2009)
DOI: 10.1016/j.amc.2009.02.059
See this article

A Non-oscillatory Central Scheme for One-Dimensional Two-Layer Shallow Water Flows along Channels with Varying Width

Jorge Balbás and Smadar Karni
Journal of Scientific Computing 55 (3) 499 (2013)
DOI: 10.1007/s10915-012-9642-3
See this article

Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam break of Aznalcóllar

M.J. Castro Díaz, T. Chacón Rebollo, E.D. Fernández-Nieto, J.M. González Vida and C. Parés
Computer Methods in Applied Mechanics and Engineering 197 (45-48) 3932 (2008)
DOI: 10.1016/j.cma.2008.03.026
See this article

Two-dimensional numerical modeling of dam-break flows over natural terrain using a central explicit scheme

Jaswant Singh, Mustafa S. Altinakar and Yan Ding
Advances in Water Resources 34 (10) 1366 (2011)
DOI: 10.1016/j.advwatres.2011.07.007
See this article

Computations of steady and unsteady transport of pollutant in shallow water

Li Cai, Jian-Hu Feng, Wen-Xian Xie and Jun Zhou
Mathematics and Computers in Simulation 71 (1) 31 (2006)
DOI: 10.1016/j.matcom.2005.10.002
See this article

Solution of 2D Shallow Water Equations by Genuinely Multidimensional Semi-Discrete Central Scheme

Jian-zhong Chen and Zhong-ke Shi
Journal of Hydrodynamics 18 (4) 436 (2006)
DOI: 10.1016/S1001-6058(06)60117-0
See this article

Multilevel finite volume methods and boundary conditions for geophysical flows

Arthur Bousquet, Martine Marion, Madalina Petcu and Roger Temam
Computers & Fluids 74 66 (2013)
DOI: 10.1016/j.compfluid.2013.01.001
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

Tracking discontinuities in shallow water equations and ideal magnetohydrodynamics equations via Ghost Fluid Method

Li Cai, Jian-Hu Feng, Wen-Xian Xie and Jun Zhou
Applied Numerical Mathematics 56 (12) 1555 (2006)
DOI: 10.1016/j.apnum.2005.11.006
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

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

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

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

Numerical modeling of submarine turbidity currents over erodible beds using unstructured grids

Xin Liu, Julio Ángel Infante Sedano and Abdolmajid Mohammadian
Ocean Modelling 113 157 (2017)
DOI: 10.1016/j.ocemod.2017.03.015
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

An improved Serre model: Efficient simulation and comparative evaluation

J.S.A. do Carmo, J.A. Ferreira, L. Pinto and G. Romanazzi
Applied Mathematical Modelling 56 404 (2018)
DOI: 10.1016/j.apm.2017.12.005
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

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

The MOOD method for the non-conservative shallow-water system

S. Clain and J. Figueiredo
Computers & Fluids 145 99 (2017)
DOI: 10.1016/j.compfluid.2016.11.013
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

High order finite volume WENO schemes for the shallow water flows through channels with irregular geometry

Yulong Xing
Journal of Computational and Applied Mathematics 299 229 (2016)
DOI: 10.1016/j.cam.2015.11.042
See this article

High Order Still-Water and Moving-Water Equilibria Preserving Discontinuous Galerkin Methods for the Ripa Model

Jolene Britton and Yulong Xing
Journal of Scientific Computing 82 (2) (2020)
DOI: 10.1007/s10915-020-01134-y
See this article

Application of positivity-preserving well-balanced discontinuous Galerkin method in computational hydrology

Xiao Wen, Zhen Gao, Wai Sun Don, Yulong Xing and Peng Li
Computers & Fluids 139 112 (2016)
DOI: 10.1016/j.compfluid.2016.04.020
See this article

Well-balanced finite difference WENO schemes for the Ripa model

Xiao Han and Gang Li
Computers & Fluids 134-135 1 (2016)
DOI: 10.1016/j.compfluid.2016.04.031
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

On Well‐Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems

M. J. Castro Díaz, T. Chacón Rebollo, E. D. Fernández‐Nieto and Carlos Parés
SIAM Journal on Scientific Computing 29 (3) 1093 (2007)
DOI: 10.1137/040607642
See this article

A central-upwind geometry-preserving method for hyperbolic conservation laws on the sphere

Abdelaziz Beljadid and Philippe LeFloch
Communications in Applied Mathematics and Computational Science 12 (1) 81 (2017)
DOI: 10.2140/camcos.2017.12.81
See this article

High order well-balanced finite difference WENO schemes for shallow water flows along channels with irregular geometry

Xiufang Wang, Gang Li, Shouguo Qian, Jiaojiao Li and Zhen Wang
Applied Mathematics and Computation 363 124587 (2019)
DOI: 10.1016/j.amc.2019.124587
See this article

A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography

Gang-feng Wu, Zhi-guo He, Liang Zhao and Guo-hua Liu
Journal of Hydrodynamics 30 (4) 618 (2018)
DOI: 10.1007/s42241-018-0069-7
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

A modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations

Aimin Chen and Maojun Li
Journal of Computational and Applied Mathematics 345 374 (2019)
DOI: 10.1016/j.cam.2018.06.033
See this article

Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels

Shouguo Qian, Gang Li, Fengjing Shao and Yulong Xing
Advances in Water Resources 115 172 (2018)
DOI: 10.1016/j.advwatres.2018.03.001
See this article

Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes

Huijing Du, Yingjie Liu, Yuan Liu and Zhiliang Xu
Journal of Scientific Computing 81 (3) 2115 (2019)
DOI: 10.1007/s10915-019-01073-3
See this article

A New Hydrostatic Reconstruction Scheme Based on Subcell Reconstructions

Guoxian Chen and Sebastian Noelle
SIAM Journal on Numerical Analysis 55 (2) 758 (2017)
DOI: 10.1137/15M1053074
See this article

Central-upwind scheme for 2D turbulent shallow flows using high-resolution meshes with scalable wall functions

Bobby Minola Ginting
Computers & Fluids 179 394 (2019)
DOI: 10.1016/j.compfluid.2018.11.014
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

Fourth-order accurate finite-volume CWENO scheme for astrophysical MHD problems

Prabal Singh Verma, Jean-Mathieu Teissier, Oliver Henze and Wolf-Christian Müller
Monthly Notices of the Royal Astronomical Society 482 (1) 416 (2019)
DOI: 10.1093/mnras/sty2641
See this article

Comparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction terms

M. Lukáčová-Medvid'ová and U. Teschke
ZAMM 86 (11) 874 (2006)
DOI: 10.1002/zamm.200510280
See this article

Mapping of Floodplain Retention and Active Flow Area in 1D Models for Large and Regional-Scale Hydrodynamic Modeling

Ireneusz Laks
Journal of Hydrologic Engineering 24 (3) 04019001 (2019)
DOI: 10.1061/(ASCE)HE.1943-5584.0001754
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

Well-Balanced Bottom Discontinuities Treatment for High-Order Shallow Water Equations WENO Scheme

Valerio Caleffi and Alessandro Valiani
Journal of Engineering Mechanics 135 (7) 684 (2009)
DOI: 10.1061/(ASCE)0733-9399(2009)135:7(684)
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

A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

Alina Chertock and Alexander Kurganov
Numerische Mathematik 111 (2) 169 (2008)
DOI: 10.1007/s00211-008-0188-0
See this article

Geometric Modelling, Numerical Simulation, and Optimization

Trond Runar Hagen, Martin O. Henriksen, Jon M. Hjelmervik and Knut-Andreas Lie
Geometric Modelling, Numerical Simulation, and Optimization 211 (2007)
DOI: 10.1007/978-3-540-68783-2_8
See this article

A well-balanced upstream flux-splitting finite-volume scheme for shallow-water flow simulations with irregular bed topography

Jihn-Sung Lai, Wen-Dar Guo, Gwo-Fong Lin and Yih-Chi Tan
International Journal for Numerical Methods in Fluids n/a (2009)
DOI: 10.1002/fld.2048
See this article

Transport of pollutant in shallow flows: A space–time CE/SE scheme

Omar Rabbani, Munshoor Ahmed and Saqib Zia
Computers & Mathematics with Applications 77 (12) 3195 (2019)
DOI: 10.1016/j.camwa.2019.02.010
See this article

Finite volume method with reconstruction and bottom modification for open channel flows: An application to Yom River, Thailand

Thida Pongsanguansin, Montri Maleewong and Khamron Mekchay
International Journal for Computational Methods in Engineering Science and Mechanics 19 (4) 227 (2018)
DOI: 10.1080/15502287.2018.1454540
See this article

Hybrid finite element/volume method for shallow water equations

Shahrouz Aliabadi, Muhammad Akbar and Reena Patel
International Journal for Numerical Methods in Engineering 83 (13) 1719 (2010)
DOI: 10.1002/nme.2886
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 new approach for fluid dynamics simulation: The Short-lived Water Cuboid Particle model

Changjian Qiao, Jiansong Li and Zongshun Tian
Journal of Hydrology 540 437 (2016)
DOI: 10.1016/j.jhydrol.2016.06.051
See this article

Hyperbolic Problems: Theory, Numerics, Applications

A. Chertock, E. Kashdan and A. Kurganov
Hyperbolic Problems: Theory, Numerics, Applications 371 (2008)
DOI: 10.1007/978-3-540-75712-2_33
See this article

Hyperbolic Problems: Theory, Numerics, Applications

A. Kurganov and G. Petrova
Hyperbolic Problems: Theory, Numerics, Applications 635 (2008)
DOI: 10.1007/978-3-540-75712-2_63
See this article

Hyperbolic Problems: Theory, Numerics, Applications

T. Gallouët
Hyperbolic Problems: Theory, Numerics, Applications 113 (2008)
DOI: 10.1007/978-3-540-75712-2_9
See this article

Well-balanced central-upwind scheme for a fully coupled shallow water system modeling flows over erodible bed

Xin Liu, Abdolmajid Mohammadian, Alexander Kurganov and Julio Angel Infante Sedano
Journal of Computational Physics 300 202 (2015)
DOI: 10.1016/j.jcp.2015.07.043
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

Lattice Boltzmann methods for shallow water flow applications

Guido Thömmes, Mohammed Seaïd and Mapundi K. Banda
International Journal for Numerical Methods in Fluids 55 (7) 673 (2007)
DOI: 10.1002/fld.1489
See this article

The role of the Rankine-Hugoniot relations in staggered finite difference schemes for the shallow water equations

Marcel Zijlema
Computers & Fluids 192 104274 (2019)
DOI: 10.1016/j.compfluid.2019.104274
See this article

A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations

Yuanzhen Cheng, Alina Chertock, Michael Herty, Alexander Kurganov and Tong Wu
Journal of Scientific Computing 80 (1) 538 (2019)
DOI: 10.1007/s10915-019-00947-w
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

IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows

Georgij Bispen, K. R. Arun, Mária Lukáčová-Medvid’ová and Sebastian Noelle
Communications in Computational Physics 16 (2) 307 (2014)
DOI: 10.4208/cicp.040413.160114a
See this article

Momentum Conservative Schemes for Shallow Water Flows

S. R. Pudjaprasetya and I. Magdalena
East Asian Journal on Applied Mathematics 4 (2) 152 (2014)
DOI: 10.4208/eajam.290913.170314a
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

Kepler shuffle for real-world flood simulations on GPUs

Zsolt Horváth, Rui AP Perdigão, Jürgen Waser, et al.
The International Journal of High Performance Computing Applications 30 (4) 379 (2016)
DOI: 10.1177/1094342016630800
See this article

A numerical model for three-dimensional shallow water flows with sharp gradients over mobile topography

Xin Liu, Abdolmajid Mohammadian and Julio Ángel Infante Sedano
Computers & Fluids 154 1 (2017)
DOI: 10.1016/j.compfluid.2017.05.021
See this article

A Well-balanced Positivity Preserving Central-upwind Scheme for Shallow Water Flows over Uneven Topography

Fanjie Wu, Gangfeng Wu and Kefeng Zhang
IOP Conference Series: Materials Science and Engineering 677 032083 (2019)
DOI: 10.1088/1757-899X/677/3/032083
See this article

Beyond Shallow Water: Appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer theory

Francesco De Vita, Pierre-Yves Lagrée, Sergio Chibbaro and Stéphane Popinet
European Journal of Mechanics - B/Fluids 79 233 (2020)
DOI: 10.1016/j.euromechflu.2019.09.010
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

Transparent boundary condition for the momentum conservative scheme of the shallow water equations

M A Ginting, S R Pudjaprasetya, D Adytia and L H Wiryanto
IOP Conference Series: Earth and Environmental Science 618 012007 (2020)
DOI: 10.1088/1755-1315/618/1/012007
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

Embedded Systems and Artificial Intelligence

Hind Talbi, El Miloud Chaabelasri, Najim Salhi and Imad Elmahi
Advances in Intelligent Systems and Computing, Embedded Systems and Artificial Intelligence 1076 75 (2020)
DOI: 10.1007/978-981-15-0947-6_8
See this article

A well-balanced central-upwind scheme for the thermal rotating shallow water equations

Alexander Kurganov, Yongle Liu and Vladimir Zeitlin
Journal of Computational Physics 411 109414 (2020)
DOI: 10.1016/j.jcp.2020.109414
See this article

Numerical Simulations of the Two-Dimensional Inviscid Hydrostatic Primitive Equations with Humidity and Saturation

Arthur Bousquet, Youngjoon Hong, Roger Temam and Joseph Tribbia
Journal of Scientific Computing 83 (2) (2020)
DOI: 10.1007/s10915-020-01215-y
See this article

One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems

Xin Liu, Alina Chertock, Alexander Kurganov and Karlan Wolfkill
Journal of Scientific Computing 81 (3) 1297 (2019)
DOI: 10.1007/s10915-019-00985-4
See this article

A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations

Gang Li, Jiaojiao Li, Shouguo Qian and Jinmei Gao
Applied Mathematics and Computation 395 125848 (2021)
DOI: 10.1016/j.amc.2020.125848
See this article

Entropy Stable and Well-Balanced Discontinuous Galerkin Methods for the Nonlinear Shallow Water Equations

Xiao Wen, Wai Sun Don, Zhen Gao and Yulong Xing
Journal of Scientific Computing 83 (3) (2020)
DOI: 10.1007/s10915-020-01248-3
See this article

An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations

Mohammad A. Ghazizadeh, Abdolmajid Mohammadian and Alexander Kurganov
Computers & Fluids 208 104633 (2020)
DOI: 10.1016/j.compfluid.2020.104633
See this article

Modified shallow water model for viscous fluids and positivity preserving numerical approximation

Elisa Biagioli, Mattia de’ Michieli Vitturi and Fabio Di Benedetto
Applied Mathematical Modelling 94 482 (2021)
DOI: 10.1016/j.apm.2020.12.036
See this article

Efficient shallow water simulations on GPUs: Implementation, visualization, verification, and validation

André R. Brodtkorb, Martin L. Sætra and Mustafa Altinakar
Computers & Fluids 55 1 (2012)
DOI: 10.1016/j.compfluid.2011.10.012
See this article

Three-dimensional shallow water system: A relaxation approach

Xin Liu, Abdolmajid Mohammadian, Julio Ángel Infante Sedano and Alexander Kurganov
Journal of Computational Physics 333 160 (2017)
DOI: 10.1016/j.jcp.2016.12.030
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

A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids

Hamidreza Shirkhani, Abdolmajid Mohammadian, Ousmane Seidou and Alexander Kurganov
Computers & Fluids 126 25 (2016)
DOI: 10.1016/j.compfluid.2015.11.017
See this article

Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows

Abdelaziz Beljadid, Abdolmajid Mohammadian and Alexander Kurganov
Computers & Fluids 136 193 (2016)
DOI: 10.1016/j.compfluid.2016.06.005
See this article

Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations

Dihan Dai, Yekaterina Epshteyn and Akil Narayan
SIAM Journal on Scientific Computing 43 (2) A929 (2021)
DOI: 10.1137/20M1360736
See this article

Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme

André R. Brodtkorb and HÅvard Heitlo Holm
Tellus A: Dynamic Meteorology and Oceanography 73 (1) 1 (2021)
DOI: 10.1080/16000870.2021.1876341
See this article

Sven-Joachim Kimmerle and Matthias Gerdts
515 (2015)
DOI: 10.3934/proc.2015.0515
See this article

1D–2D Numerical Model for Wave Attenuation by Mangroves as a Porous Structure

Ikha Magdalena, Vivianne Kusnowo, Moh. Ivan Azis and Widowati
Computation 9 (6) 66 (2021)
DOI: 10.3390/computation9060066
See this article