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.
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.
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Jorge San Martín 1; Jean-François Scheid 2; Loredana Smaranda 3
@article{CRMATH_2010__348_15-16_935_0, author = {Jorge San Mart{\'\i}n and Jean-Fran\c{c}ois Scheid and Loredana Smaranda}, 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}, }
TY - JOUR AU - Jorge San Martín AU - Jean-François Scheid AU - Loredana Smaranda 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 DO - 10.1016/j.crma.2010.07.004 LA - en ID - CRMATH_2010__348_15-16_935_0 ER -
%0 Journal Article %A Jorge San Martín %A Jean-François Scheid %A Loredana Smaranda %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 %R 10.1016/j.crma.2010.07.004 %G en %F CRMATH_2010__348_15-16_935_0
Jorge San Martín; Jean-François Scheid; Loredana Smaranda. A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 935-939. doi : 10.1016/j.crma.2010.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.004/
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