[Schéma semi-implicite sur maillages décalés pour le système shallow water multi-couches]
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.
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@article{CRMATH_2017__355_12_1298_0,
author = {Duran, Arnaud and Vila, Jean-Paul and Baraille, R\'emy},
title = {Semi-implicit staggered mesh scheme for the multi-layer shallow water system},
journal = {Comptes Rendus. Math\'ematique},
pages = {1298--1306},
publisher = {Elsevier},
volume = {355},
number = {12},
year = {2017},
doi = {10.1016/j.crma.2017.09.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.09.011/}
}
TY - JOUR AU - Duran, Arnaud AU - Vila, Jean-Paul AU - Baraille, Rémy TI - Semi-implicit staggered mesh scheme for the multi-layer shallow water system JO - Comptes Rendus. Mathématique PY - 2017 SP - 1298 EP - 1306 VL - 355 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.09.011/ DO - 10.1016/j.crma.2017.09.011 LA - en ID - CRMATH_2017__355_12_1298_0 ER -
%0 Journal Article %A Duran, Arnaud %A Vila, Jean-Paul %A Baraille, Rémy %T Semi-implicit staggered mesh scheme for the multi-layer shallow water system %J Comptes Rendus. Mathématique %D 2017 %P 1298-1306 %V 355 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.09.011/ %R 10.1016/j.crma.2017.09.011 %G en %F CRMATH_2017__355_12_1298_0
Duran, Arnaud; Vila, Jean-Paul; Baraille, Rémy. Semi-implicit staggered mesh scheme for the multi-layer shallow water system. Comptes Rendus. Mathématique, Tome 355 (2017) no. 12, pp. 1298-1306. doi : 10.1016/j.crma.2017.09.011. http://www.numdam.org/articles/10.1016/j.crma.2017.09.011/
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