Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

Abstract

International audienceA new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as ''tank treading'' and tumbling motions

Eulerian model of immersed elastic surfaces with full membrane elasticity

“…For simple vesicles, the involved energy is a curvature energy, which is minimized with an area and enclosed volume constraint. In that case, Eulerian and Lagrangian models were developed in the last decade and proved to successfully reproduce the dynamics of such objects in flow [5,8,7,9,6,11]. For the red blood cells the cytoskeleton provides an extra resistance to membrane shear.…”

Simulation of vesicle using level set method solved by high order finite element

“…In many models, the local area of the vesicle is conserved by adding a Lagrange multiplier which ensures the membrane inextensibility as in [5,17,20,21]. In [22,23], the authors show the possibility to get the quasi inextensibility of the membrane by adding an elastic force using the derivative of an elastic energy.…”

“…A validation of our two-fluid model based on Navier-Stokes equations and the level set advection has been presented in [17] on a bubble simulation benchmark. In this work we also consider the Stokes equations.…”

Derivation of nonlinear shell models combining shear and flexure: application to biological membranes

“…Another approach based on the immersed boundary method has been investigated by Kim and Lai [2010], and, together with a lattice Boltzmann approach, by Crowl and Fogelson [2010]. Finally, level set methods have also been implemented in this context by Salac and Miksis [2011], and Maitre, Milcent, Cottet, Raoult and Usson [Maitre et al 2009] (see also [Doyeux et al 2013] We prove in this article that the classical mechanical model of the RBCs can be recovered by means of a formal asymptotic analysis assuming that the RBC's membrane is made of a locally homogeneous, albeit strongly anisotropic, nonlinearly elastic material. The main difference with previous works on the justification of thin structures is that we assume different scalings for the elastic moduli in the tangential and normal directions to the midsection.…”