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Comptes Rendus Mathématique
Volume 352, n° 11
pages 953-957 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.020
Received : 12 June 2014 ;  accepted : 22 September 2014
Numerical scheme for multilayer shallow-water model in the low-Froude number regime
Schéma numérique pour les modèles de Saint-Venant multi-couche à faible nombre de Froude
 

Martin Parisot a , Jean-Paul Vila b
a Institut de mathématiques de Toulouse, UMR CNRS 5219, UPS IMT, 31062 Toulouse cedex 9, France 
b Institut de mathématiques de Toulouse, UMR CNRS 5219, INSA, 31077 Toulouse, France 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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 full text of this article is available in PDF format.

 This work was supported by the French Naval Hydrographic and Oceanographic Service (grant number N11CR0001).



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