Dynamics of biomembranes using level set and adaptive finite element methods

Aymen Laadhari (1) , Pierre Saramito (1) , Chaouqi Misbah (2)

1 LJK - Laboratoire Jean Kuntzmann
2 LSP - Laboratoire de Spectrométrie Physique

The numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper. A new saddle-point approach is proposed for the imposition if the fluid incompressibility and the membrane inextensibility constraints, through Lagrange multipliers defined in the fluid and on the membrane respectively. Using a level set formulation, the problem is approximated with mixed finite elements combined with an automatic adaptive mesh procedure at the vicinity of the membrane boundary. Numerical experiments show that this combination of the saddle-point and adaptive mesh method enhances the accuracy of the method.

Mots clés: finite element; mesh adaptation; shape optimization; Helfrich energy; fluid mechanics; interface; level set method; vesicle; blood flow

Domaines: Analyse numérique [math.NA]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Physique Numérique [physics.comp-ph]; Biophysique [physics.bio-ph]; Dynamique des Fluides [physics.flu-dyn]

Aymen Laadhari, Pierre Saramito, Chaouqi Misbah. Dynamics of biomembranes using level set and adaptive finite element methods. 2011. ⟨hal-00604145v1⟩