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A robust well-balanced scheme for multi-layer shallow water equations
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Preface
Large-scale vorticity generation due to dissipating waves in the surf zone
1. | Université Bordeaux 1, CNRS, UMR 5805-EPOC, avenue des Facultés, Talence, F-33405, France, France, France |
2. | Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugene Bataillon, 34095 Montpellier cedex 5, France |
[1] |
Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89 |
[2] |
Marie-Odile Bristeau, Jacques Sainte-Marie. Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733 |
[3] |
Darryl D. Holm, Ruiao Hu. Nonlinear dispersion in wave-current interactions. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022004 |
[4] |
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie, Mohammed Seaid. Multilayer Saint-Venant equations over movable beds. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 917-934. doi: 10.3934/dcdsb.2011.15.917 |
[5] |
Georges Bastin, Jean-Michel Coron, Brigitte d'Andréa-Novel. On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Networks and Heterogeneous Media, 2009, 4 (2) : 177-187. doi: 10.3934/nhm.2009.4.177 |
[6] |
Julien Chambarel, Christian Kharif, Olivier Kimmoun. Focusing wave group in shallow water in the presence of wind. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 773-782. doi: 10.3934/dcdsb.2010.13.773 |
[7] |
Xue Yang, Xinglong Wu. Wave breaking and persistent decay of solution to a shallow water wave equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2149-2165. doi: 10.3934/dcdss.2016089 |
[8] |
Denys Dutykh, Delia Ionescu-Kruse. Effects of vorticity on the travelling waves of some shallow water two-component systems. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5521-5541. doi: 10.3934/dcds.2019225 |
[9] |
Delia Ionescu-Kruse. Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 531-543. doi: 10.3934/dcds.2007.19.531 |
[10] |
Anna Geyer, Ronald Quirchmayr. Traveling wave solutions of a highly nonlinear shallow water equation. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1567-1604. doi: 10.3934/dcds.2018065 |
[11] |
E. Audusse. A multilayer Saint-Venant model: Derivation and numerical validation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 189-214. doi: 10.3934/dcdsb.2005.5.189 |
[12] |
Hassen Arfaoui, Faker Ben Belgacem, Henda El Fekih, Jean-Pierre Raymond. Boundary stabilizability of the linearized viscous Saint-Venant system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 491-511. doi: 10.3934/dcdsb.2011.15.491 |
[13] |
George Dassios, Michalis N. Tsampas. Vector ellipsoidal harmonics and neuronal current decomposition in the brain. Inverse Problems and Imaging, 2009, 3 (2) : 243-257. doi: 10.3934/ipi.2009.3.243 |
[14] |
Hung-Chu Hsu. Exact azimuthal internal waves with an underlying current. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4391-4398. doi: 10.3934/dcds.2017188 |
[15] |
Sharif E. Guseynov, Eugene A. Kopytov, Edvin Puzinkevich. On continuous models of current stock of divisible productions. Conference Publications, 2011, 2011 (Special) : 601-613. doi: 10.3934/proc.2011.2011.601 |
[16] |
Amir Moradifam, Robert Lopez. Stability of current density impedance imaging II. Communications on Pure and Applied Analysis, 2021, 20 (11) : 4025-4041. doi: 10.3934/cpaa.2021142 |
[17] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[18] |
Zhigang Wang. Vanishing viscosity limit of the rotating shallow water equations with far field vacuum. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 311-328. doi: 10.3934/dcds.2018015 |
[19] |
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593 |
[20] |
Denys Dutykh, Dimitrios Mitsotakis. On the relevance of the dam break problem in the context of nonlinear shallow water equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 799-818. doi: 10.3934/dcdsb.2010.13.799 |
2021 Impact Factor: 1.497
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