ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

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

Cottet, Georges-Henria1, Maitre, Emmanuela1 and Milcent, Thomasa1

a1 Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France. georges-henri.cottet@imap.fr

Abstract

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.

(Received July 25 2007)

(Revised December 20 2007)

(Online publication April 3 2008)

Key Words:

  • Fluid structure interaction;
  • elastic membrane;
  • Eulerian method;
  • level set method;
  • Korteweg fluid;
  • Navier-Stokes equations.

Mathematics Subject Classification:

  • 76D05;
  • 74B20;
  • 74F10
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