Eulerian formulation and level set models for incompressible fluid-structure interaction
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 8041 Grenoble Cedex 9, France. firstname.lastname@example.org
Revised: 20 December 2007
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.
Mathematics Subject Classification: 76D05 / 74B20 / 74F10
Key words: Fluid structure interaction / elastic membrane / Eulerian method / level set method / Korteweg fluid / Navier-Stokes equations.
© EDP Sciences, SMAI, 2008