Geodesic
Eulerian formulation and level set models for incompressible fluid-structure interaction
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 471-492

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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.

DOI : 10.1051/m2an:2008013
Classification : 76D05, 74B20, 74F10
Keywords: fluid structure interaction, elastic membrane, eulerian method, level set method, Korteweg fluid, Navier-Stokes equations 
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     title = {Eulerian formulation and level set models for incompressible fluid-structure interaction},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {471--492},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     doi = {10.1051/m2an:2008013},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008013/}
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Cottet, Georges-Henri; Maitre, Emmanuel; Milcent, Thomas. Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 471-492. doi: 10.1051/m2an:2008013

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