Eulerian formulation and level set models for incompressible fluid-structure interaction
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, p. 471-492

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.

DOI : https://doi.org/10.1051/m2an:2008013
Classification:  76D05,  74B20,  74F10
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
pages = {471-492},
doi = {10.1051/m2an:2008013},
zbl = {pre05288668},
mrnumber = {2423795},
language = {en},
url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, pp. 471-492. doi : 10.1051/m2an:2008013. http://www.numdam.org/item/M2AN_2008__42_3_471_0/

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