[Discrétisation en temps d'une méthode de caractéristiques pour un système d'interaction fluide–rigide avec densité discontinue]
Nous présentons un schéma de semi-discrétisation en temps d'une méthode de caractéristiques pour un problème fluide–rigide dans le cas où les densités du fluide et du solide sont différentes. Cette méthode est basée sur une formulation faible globale faisant intervenir uniquement des termes définis sur tout le domaine fluide–rigide. L'idée principale est de construire une fonction caractéristique qui préserve la rigidité du solide d'une itération en temps à l'autre. Le résultat principal porte sur la convergence du schéma semi-discrétisé en temps.
We propose a new characteristics method for the time discretization of a fluid–rigid system in the case when the densities of the fluid and the solid are different. This method is based on a global weak formulation involving only terms defined on the whole fluid–rigid domain. The main idea is to construct a characteristic function which preserves the rigidity of the solid at the discrete time levels. A convergence result for this semi-discrete scheme is then given.
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@article{CRMATH_2010__348_15-16_935_0,
author = {San Mart{\'\i}n, Jorge and Scheid, Jean-Fran\c{c}ois and Smaranda, Loredana},
title = {A time discretization scheme of a characteristics method for a fluid{\textendash}rigid system with discontinuous density},
journal = {Comptes Rendus. Math\'ematique},
pages = {935--939},
publisher = {Elsevier},
volume = {348},
number = {15-16},
year = {2010},
doi = {10.1016/j.crma.2010.07.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.004/}
}
TY - JOUR AU - San Martín, Jorge AU - Scheid, Jean-François AU - Smaranda, Loredana TI - A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density JO - Comptes Rendus. Mathématique PY - 2010 SP - 935 EP - 939 VL - 348 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.004/ DO - 10.1016/j.crma.2010.07.004 LA - en ID - CRMATH_2010__348_15-16_935_0 ER -
%0 Journal Article %A San Martín, Jorge %A Scheid, Jean-François %A Smaranda, Loredana %T A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density %J Comptes Rendus. Mathématique %D 2010 %P 935-939 %V 348 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.004/ %R 10.1016/j.crma.2010.07.004 %G en %F CRMATH_2010__348_15-16_935_0
San Martín, Jorge; Scheid, Jean-François; Smaranda, Loredana. A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density. Comptes Rendus. Mathématique, Tome 348 (2010) no. 15-16, pp. 935-939. doi : 10.1016/j.crma.2010.07.004. http://www.numdam.org/articles/10.1016/j.crma.2010.07.004/
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