Eulerian formulation and level set models for incompressible fluid-structure interaction

Georges-Henri Cottet (1) , Emmanuel Maitre (1) , Thomas Milcent (1)

1 EDP - Equations aux Dérivées Partielles

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; level set methods; korteweg fluids

Domaines: Analyse numérique [math.NA]

Georges-Henri Cottet, Emmanuel Maitre, Thomas Milcent. Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM: Mathematical Modelling and Numerical Analysis, 2008, 42 (3), pp.471-492. ⟨10.1051/m2an:2008013⟩. ⟨hal-00297711⟩