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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 ,
Emmanuel Maitre  and
Thomas Milcent
Georges-Henri Cottet
Affiliation:
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France. georges-henri.cottet@imap.fr
Emmanuel Maitre
Affiliation:
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France. georges-henri.cottet@imap.fr
Thomas Milcent
Affiliation:
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France. georges-henri.cottet@imap.fr
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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.

Keywords

Fluid structure interactionelastic membraneEulerian methodlevel set methodKorteweg fluidNavier-Stokes equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 3 , May 2008 , pp. 471 - 492
Copyright
© EDP Sciences, SMAI, 2008

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