Comptes Rendus
Numerical analysis
Semi-implicit staggered mesh scheme for the multi-layer shallow water system
[Schéma semi-implicite sur maillages décalés pour le système shallow water multi-couches]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1298-1306.

Nous proposons un schéma semi-implicite destiné à un modèle shallow water multicouches 2d avec stratification en densité, formulé sur maillages décalés généraux. Le principal résultat de cette note concerne le contrôle de l'énergie mécanique au niveau discret, qui se base principalement sur des flux advectifs faisant intervenir un terme de diffusion exprimé en fonction du gradient de pression. Le schéma est aussi conçu pour capturer les dynamiques des régimes à faible nombre de Froude et offre d'intéressantes propriétés en termes de positivité et préservation des états d'équilibre. Un test numérique est proposé pour illustrer l'efficacité du schéma dans le cas monocouche.

We present a semi-implicit scheme for a two-dimensional multilayer shallow water system with density stratification, formulated on general staggered meshes. The main result of the present note concerns the control of the mechanical energy at the discrete level, principally based on advective fluxes implying a diffusion term expressed in terms of the gradient pressure. The scheme is also designed to capture the dynamics of low-Froude-number regimes and offers interesting positivity and well-balancing results. A numerical test is proposed to highlight the scheme's efficiency in the one-layer case.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.011

Arnaud Duran 1 ; Jean-Paul Vila 2, 3 ; Rémy Baraille 2, 3, 4

1 Institut Camille-Jordan, Université Claude-Bernard, Lyon-1, France
2 Institut de mathématiques de Toulouse, Université Paul-Sabatier, Toulouse-3, France
3 INSA, Institut de mathématiques de Toulouse, Université Paul-Sabatier, Toulouse-3, France
4 Service hydrographique et océanographique de la Marine, France
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     title = {Semi-implicit staggered mesh scheme for the multi-layer shallow water system},
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Arnaud Duran; Jean-Paul Vila; Rémy Baraille. Semi-implicit staggered mesh scheme for the multi-layer shallow water system. Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1298-1306. doi : 10.1016/j.crma.2017.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.011/

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