Numerical scheme for multilayer shallow-water model in the low-Froude number regime

Parisot, Martin; Vila, Jean-Paul

Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 953-957.

Le but de cette note est de présenter un schéma numérique multi-dimensionnel rapprochant les solutions du modèle de Saint-Venant multi-couche en régime de faible nombre de Froude. La stratégie proposée est basée sur un modèle régularisé où la vitesse de transport est modifiée par un gradient de pression dans les équations de la masse et de la quantité de mouvement. La solution numérique satisfait la dissipation d'énergie, jouant le rôle de l'entropie du point de vue mathématique, et les principales propriétés physiques nécessaires aux simulations dans le cadre des écoulements océaniques.

The aim of this note is to present a multi-dimensional numerical scheme approximating the solutions to the multilayer shallow-water model in the low-Froude-number regime. The proposed strategy is based on a regularized model where the advection velocity is modified with a pressure gradient in both mass and momentum equations. The numerical solution satisfies the dissipation of energy, which acts for mathematical entropy, and the main physical properties required for simulations within oceanic flows.

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