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A robust numerical scheme based on auxiliary interface variables and monotone-preserving reconstructions for two-layer shallow water equations with wet–dry fronts
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A well‐balanced positivity‐preserving central‐upwind scheme for one‐dimensional blood flow models
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A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels
Gerardo Hernandez-Duenas and Jorge Balbás ESAIM: Mathematical Modelling and Numerical Analysis 55(5) 2185 (2021) https://doi.org/10.1051/m2an/2021052
A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet–dry treatment
Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts
J. Murillo, S. Martinez-Aranda, A. Navas-Montilla and P. García-Navarro Journal of Hydroinformatics 22(5) 972 (2020) https://doi.org/10.2166/hydro.2020.207
Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface
Sebastien Allgeyer, Marie-Odile Bristeau, David Froger, et al. ESAIM: Mathematical Modelling and Numerical Analysis 53(6) 1981 (2019) https://doi.org/10.1051/m2an/2019044
Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities
Christophe Berthon, Arnaud Duran, Françoise Foucher, Khaled Saleh and Jean De Dieu Zabsonré Journal of Scientific Computing 80(2) 924 (2019) https://doi.org/10.1007/s10915-019-00961-y
A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model
Eirik Holm Fyhn, Karl Yngve Lervåg, Åsmund Ervik and Øivind Wilhelmsen Physics of Fluids 31(12) (2019) https://doi.org/10.1063/1.5126168
A Two‐Layer Hydrostatic‐Reconstruction Method for High‐Resolution Solving of the Two‐Layer Shallow‐Water Equations over Uneven Bed Topography
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) https://doi.org/10.1051/m2an/2018077
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 compressible two-layer model for transient gas–liquid flows in pipes
Convergence Improved Lax-Friedrichs Scheme Based Numerical Schemes and Their Applications in Solving the One-Layer and Two-Layer Shallow-Water Equations
Xinhua Lu, Bingjiang Dong, Bing Mao and Xiaofeng Zhang Mathematical Problems in Engineering 2015 1 (2015) https://doi.org/10.1155/2015/379281
An efficient splitting technique for two-layer shallow-water model
Christophe Berthon, Françoise Foucher and Tomás Morales Numerical Methods for Partial Differential Equations 31(5) 1396 (2015) https://doi.org/10.1002/num.21949
Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing
A new composite scheme for two-layer shallow water flows with shocks
Nouh Izem, Fayssal Benkhaldoun, Slah Sahmim, Mohammed Seaid and Mohamed Wakrim Journal of Applied Mathematics and Computing 44(1-2) 467 (2014) https://doi.org/10.1007/s12190-013-0703-z
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
A fast finite volume solver for multi-layered shallow water flows with mass exchange
Emmanuel Audusse, Fayssal Benkhaldoun, Saida Sari, Mohammed Seaid and Pablo Tassi Journal of Computational Physics 272 23 (2014) https://doi.org/10.1016/j.jcp.2014.04.026
A simple multi-layer finite volume solver for density-driven shallow water flows
THREE-LAYER APPROXIMATION OF TWO-LAYER SHALLOW WATER EQUATIONS
Alina Chertock, Alexander Kurganov, Alexander Kurganov, Zhuolin Qu and Tong Wu Mathematical Modelling and Analysis 18(5) 675 (2013) https://doi.org/10.3846/13926292.2013.869269
Air entrainment in transient flows in closed water pipes : A two-layer approach
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Central Schemes for Nonconservative Hyperbolic Systems
M. J. Castro, Carlos Parés, Gabriella Puppo and Giovanni Russo SIAM Journal on Scientific Computing 34(5) B523 (2012) https://doi.org/10.1137/110828873
Numerical Treatment of the Loss of Hyperbolicity of the Two-Layer Shallow-Water System
M. J. Castro-Díaz, E. D. Fernández-Nieto, J. M. González-Vida and C. Parés-Madroñal Journal of Scientific Computing 48(1-3) 16 (2011) https://doi.org/10.1007/s10915-010-9427-5
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System
Computational Science and High Performance Computing IV
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Multilayer Saint-Venant equations over movable beds
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie and Mohammed Seaid Discrete & Continuous Dynamical Systems - B 15(4) 917 (2011) https://doi.org/10.3934/dcdsb.2011.15.917
Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help
Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 2. Active lower layer