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Computers & Fluids 134-135 1 (2016)
DOI: 10.1016/j.compfluid.2016.04.031
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Hyperbolic Problems: Theory, Numerics, Applications

T. Gallouët
Hyperbolic Problems: Theory, Numerics, Applications 113 (2008)
DOI: 10.1007/978-3-540-75712-2_9
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

Alberto Prieto-Arranz, Luis Ramírez, Iván Couceiro, Ignasi Colominas and Xesús Nogueira
Journal of Scientific Computing 88 (3) (2021)
DOI: 10.1007/s10915-021-01600-1
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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
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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
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High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction

Ruize Yang, Yang Yang and Yulong Xing
Journal of Computational Physics 444 110543 (2021)
DOI: 10.1016/j.jcp.2021.110543
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Sven-Joachim Kimmerle and Matthias Gerdts
515 (2015)
DOI: 10.3934/proc.2015.0515
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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
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A well-balanced positivity-preserving numerical scheme for shallow water models with variable density

Amine Hanini, Abdelaziz Beljadid and Driss Ouazar
Computers & Fluids 231 105156 (2021)
DOI: 10.1016/j.compfluid.2021.105156
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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)
DOI: 10.1088/1757-899X/677/3/032083
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Propagation of diffusing pollutant by kinetic flux-vector splitting method

Saqib Zia, Omar Rabbani, Asad Rehman and Munshoor Ahmed
International Journal of Nonlinear Sciences and Numerical Simulation (2021)
DOI: 10.1515/ijnsns-2019-0169
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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 (1) 012007 (2020)
DOI: 10.1088/1755-1315/618/1/012007
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