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:

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)
https://doi.org/10.1007/s10915-019-00985-4

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 (3) 032083 (2019)
https://doi.org/10.1088/1757-899X/677/3/032083

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)
https://doi.org/10.1016/j.amc.2019.124587

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)
https://doi.org/10.1016/j.cam.2018.06.033

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)
https://doi.org/10.1016/j.camwa.2019.02.010

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

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)
https://doi.org/10.1007/s10915-017-0567-8

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)
https://doi.org/10.1007/s42241-018-0069-7

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)
https://doi.org/10.1016/j.apm.2017.12.005

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)
https://doi.org/10.1080/15502287.2018.1454540

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)
https://doi.org/10.1016/j.advwatres.2018.03.001

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

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

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

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)
https://doi.org/10.1016/j.compfluid.2017.05.021

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)
https://doi.org/10.2140/camcos.2017.12.81

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)
https://doi.org/10.1016/j.jcp.2016.12.030

A New Hydrostatic Reconstruction Scheme Based on Subcell Reconstructions

Guoxian Chen and Sebastian Noelle
SIAM Journal on Numerical Analysis 55 (2) 758 (2017)
https://doi.org/10.1137/15M1053074

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)
https://doi.org/10.1007/s10915-016-0329-z

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

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)
https://doi.org/10.1016/j.ocemod.2017.03.015

Kepler shuffle for real-world flood simulations on GPUs

Zsolt Horváth, Rui AP Perdigão, Jürgen Waser, Daniel Cornel, Artem Konev and Günter Blöschl
The International Journal of High Performance Computing Applications 30 (4) 379 (2016)
https://doi.org/10.1177/1094342016630800

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)
https://doi.org/10.1016/j.compfluid.2016.04.020

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 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

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)
https://doi.org/10.1016/j.compfluid.2016.06.005

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)
https://doi.org/10.1016/j.cam.2015.11.042

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)
https://doi.org/10.1016/j.compfluid.2015.11.017

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)
https://doi.org/10.1016/bs.hna.2016.09.008

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)
https://doi.org/10.1002/fld.4023

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

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 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)
https://doi.org/10.1002/fld.3983

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)
https://doi.org/10.1016/j.jcp.2015.07.043

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

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)
https://doi.org/10.3390/w7084283

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)
https://doi.org/10.1137/151005798

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)
https://doi.org/10.1002/fld.4011

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

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)
https://doi.org/10.4208/cicp.040413.160114a

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

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

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)
https://doi.org/10.1007/s00211-014-0622-4

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

Sheng Bi, Jianzhong Zhou, Yi Liu, Lixiang Song and Hari M. Srivastava
Mathematical Problems in Engineering 2014 (1) (2014)
https://doi.org/10.1155/2014/209562

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

Gangfeng Wu, Zhiguo He, Guohua Liu and Yonghong Wu
Mathematical Problems in Engineering 2014 (1) (2014)
https://doi.org/10.1155/2014/257915

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

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

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)
https://doi.org/10.1007/s10915-012-9642-3

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

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)
https://doi.org/10.1016/j.envsoft.2013.03.003

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)
https://doi.org/10.3846/13926292.2013.869269

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

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)
https://doi.org/10.1007/s10915-013-9695-y

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)
https://doi.org/10.1016/j.compfluid.2011.10.012

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)
https://doi.org/10.1029/2010JC006315

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

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)
https://doi.org/10.1016/j.advwatres.2011.07.007

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

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)
https://doi.org/10.1007/s00791-010-0149-x

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

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 62 (8) 927 (2010)
https://doi.org/10.1002/fld.2048

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)
https://doi.org/10.1016/j.physa.2010.05.003

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)
https://doi.org/10.1002/nme.2886

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)
https://doi.org/10.1016/j.ocemod.2010.02.006

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)
https://doi.org/10.1016/j.cma.2010.07.003

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)
https://doi.org/10.1016/j.advwatres.2010.08.005

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

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

R. Touma
Applied Mathematics and Computation 213 (1) 47 (2009)
https://doi.org/10.1016/j.amc.2009.02.059

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

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