This paper is devoted to eulerian models for incompressible fluid-structure systems. These models are primarily derived for computational purposes as they allow to simulate in a rather straightforward way complex 3D systems. We first analyze the level set model of immersed membranes proposed in [Cottet and Maitre, Math. Models Methods Appl. Sci. 16 (2006) 415-438]. We in particular show that this model can be interpreted as a generalization of so-called Korteweg fluids. We then extend this model to more generic fluid-structure systems. In this framework, assuming anisotropy, the membrane model appears as a formal limit system when the elastic body width vanishes. We finally provide some numerical experiments which illustrate this claim.
Mots clés : fluid structure interaction, elastic membrane, eulerian method, level set method, Korteweg fluid, Navier-Stokes equations
@article{M2AN_2008__42_3_471_0, author = {Cottet, Georges-Henri and Maitre, Emmanuel and Milcent, Thomas}, title = {Eulerian formulation and level set models for incompressible fluid-structure interaction}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {471--492}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/m2an:2008013}, mrnumber = {2423795}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008013/} }
TY - JOUR AU - Cottet, Georges-Henri AU - Maitre, Emmanuel AU - Milcent, Thomas TI - Eulerian formulation and level set models for incompressible fluid-structure interaction JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 471 EP - 492 VL - 42 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008013/ DO - 10.1051/m2an:2008013 LA - en ID - M2AN_2008__42_3_471_0 ER -
%0 Journal Article %A Cottet, Georges-Henri %A Maitre, Emmanuel %A Milcent, Thomas %T Eulerian formulation and level set models for incompressible fluid-structure interaction %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 471-492 %V 42 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008013/ %R 10.1051/m2an:2008013 %G en %F M2AN_2008__42_3_471_0
Cottet, Georges-Henri; Maitre, Emmanuel; Milcent, Thomas. Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 471-492. doi : 10.1051/m2an:2008013. http://www.numdam.org/articles/10.1051/m2an:2008013/
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