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

Published online by Cambridge University Press:  03 April 2008

Georges-Henri Cottet
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France.
Emmanuel Maitre
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France.
Thomas Milcent
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France.
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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.

Research Article
© EDP Sciences, SMAI, 2008

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