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.Mathematics Subject Classification. 76D05, 74B20, 74F10.
This paper is devoted to the derivation and the validation of a level set method for fluidstructure interaction problems with immersed surfaces. The test case of a pressurized membrane is used to compare our method to Peskin's Immersed Boundary methods in the two-dimensional case and to demonstrate its capabilities for three-dimensional flows. The method in particular exhibits appealing mass and energy conservation properties.
rapport interne MAP5 2007-13, accepté pour publication dans Mathematical and Computer ModellingInternational audienceWe describe in this paper two applications of Eulerian level set methods to fluid-structure problems arising in biophysics. The first one is concerned with three-dimensional equilibrium shapes of phospholipidic vesicles. This is a complex problem which can be recast as the minimization of the curvature energy of an immersed elastic membrane, under a constant area constraint. The second deals with isolated cardiomyocyte contraction. This problem corresponds to a generic incompressible fluid-structure coupling between an elastic body and a fluid. By the choice of these two quite different situations, we aim to bring evidences that Eulerian methods provide efficient and flexible computational tools in biophysics applications
International audiencePhospholipidic membranes and vesicles constitute a basic element in real biological functions. Vesicles are viewed as a model system to mimic basic viscoelastic behaviors of some cells, like red blood cells. Phase field and level-set models are powerful tools to tackle dynamics of membranes and their coupling to the flow. These two methods are somewhat similar, but to date no bridge between them has been made. This is a first focus of this paper, where we show how the phase-field methods developed in Biben and Misbah (2003) [7], Beaucourt (2004) [9], Biben (2005) [33] for immersed vesicles could be considered as a level-set method for a particular strain-stress relationship. The main conclusion is that the two methods share several common features and we shall provide the correspondence between the two methods. Furthermore, a constitutive viscoelastic law is derived for the composite fluid: the ambient fluid and the membranes. We present two different approaches to deal with the membrane local incompressibility, and point out differences. Some numerical results following from the level-set approach are presented
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.