[Un algorithme de projection pour des problèmes d'interaction fluide–structure avec fort effet de masse ajoutée]
Dans cette Note nous introduisons un schéma semi-implicite pour des problèmes d'interaction fluide–structure avec un fort effet de masse-ajoutée. La méthode est basée sur un certain découplage de la masse ajoutée, des effets visqueux et des non linéarités géometriques et convectives. Ce découplage peut être obtenu par une méthode de projection type Chorin–Temam. Nous énonçons un résultat de stabilité dans un cadre linéaire, et nous présentons quelques simulations numériques. Le principal intérêt de l'algorithme proposé est son efficacité par rapport aux approches implicites.
This Note aims at introducing a semi-implicit coupling scheme for fluid–structure interaction problems with a strong added-mass effect. Our main idea relies on the splitting of added-mass, viscous effects and geometrical/convective non-linearities, through a Chorin–Temam projection scheme within the fluid. We state some theoretical stability results, in the linear case, and provide some numerical experiments. The main interest of the proposed scheme is its efficiency compared to the implicit approach.
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@article{CRMATH_2006__342_4_279_0,
author = {Fern\'andez, Miguel A. and Gerbeau, Jean-Fr\'ed\'eric and Grandmont, C\'eline},
title = {A projection algorithm for fluid{\textendash}structure interaction problems with strong added-mass effect},
journal = {Comptes Rendus. Math\'ematique},
pages = {279--284},
publisher = {Elsevier},
volume = {342},
number = {4},
year = {2006},
doi = {10.1016/j.crma.2005.12.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.017/}
}
TY - JOUR AU - Fernández, Miguel A. AU - Gerbeau, Jean-Frédéric AU - Grandmont, Céline TI - A projection algorithm for fluid–structure interaction problems with strong added-mass effect JO - Comptes Rendus. Mathématique PY - 2006 SP - 279 EP - 284 VL - 342 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.12.017/ DO - 10.1016/j.crma.2005.12.017 LA - en ID - CRMATH_2006__342_4_279_0 ER -
%0 Journal Article %A Fernández, Miguel A. %A Gerbeau, Jean-Frédéric %A Grandmont, Céline %T A projection algorithm for fluid–structure interaction problems with strong added-mass effect %J Comptes Rendus. Mathématique %D 2006 %P 279-284 %V 342 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.12.017/ %R 10.1016/j.crma.2005.12.017 %G en %F CRMATH_2006__342_4_279_0
Fernández, Miguel A.; Gerbeau, Jean-Frédéric; Grandmont, Céline. A projection algorithm for fluid–structure interaction problems with strong added-mass effect. Comptes Rendus. Mathématique, Tome 342 (2006) no. 4, pp. 279-284. doi : 10.1016/j.crma.2005.12.017. http://www.numdam.org/articles/10.1016/j.crma.2005.12.017/
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Cité par Sources :
⁎ This work has been carried out during a one-year délégation of C. Grandmont at INRIA, and partially supported by the European Community through the Research Training Network “Mathematical Modelling of the Cardiovascular System (HaeMOdel)”, contract HPRN-CT-2002-00270.
