A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 1, p. 169-200

The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.

DOI : https://doi.org/10.1051/m2an/2010036
Classification:  35Q30,  35Q35,  76D05
Keywords: Navier-Stokes equations, Saint-Venant equations, free surface, multilayer system, kinetic scheme
@article{M2AN_2011__45_1_169_0,
     author = {Audusse, Emmanuel and Bristeau, Marie-Odile and Perthame, Beno\^\i t and Sainte-Marie, Jacques},
     title = {A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {1},
     year = {2011},
     pages = {169-200},
     doi = {10.1051/m2an/2010036},
     zbl = {1290.35194},
     mrnumber = {2781135},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_1_169_0}
}
Audusse, Emmanuel; Bristeau, Marie-Odile; Perthame, Benoît; Sainte-Marie, Jacques. A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 1, pp. 169-200. doi : 10.1051/m2an/2010036. http://www.numdam.org/item/M2AN_2011__45_1_169_0/

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