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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
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
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
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
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
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
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
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
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
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
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
Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms
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 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
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
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
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
A higher-order macroscopic model for pedestrian flows
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
Augmented Riemann solver for urethra flow modeling
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