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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
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
Theory, Numerics and Applications of Hyperbolic Problems I
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A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography
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
Higher Order Finite Volume Central Schemes for Multi-dimensional Hyperbolic Problems
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
Y. Xing Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 361 (2017) https://doi.org/10.1016/bs.hna.2016.09.003
A New Hydrostatic Reconstruction Scheme Based on Subcell Reconstructions
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
Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography
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
A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids
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
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
Application of positivity-preserving well-balanced discontinuous Galerkin method in computational hydrology
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
A robust and well‐balanced scheme for the 2D Saint‐Venant system on unstructured meshes with friction source term
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
High-order well-balanced central WENO scheme for pre-balanced shallow water equations
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
Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
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 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
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
Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling
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 ‘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
Three-Layer Approximation of Two-Layer Shallow Water Equations
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 and energy stable schemes for the shallow water equations with discontinuous topography
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
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms
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
A multilevel method for finite volume discretization of the two-dimensional nonlinear shallow-water equations
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
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
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 higher-order macroscopic model for pedestrian flows
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) https://doi.org/10.1016/j.cma.2008.03.026
Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation