Finite-Element Method for the Simulation of Lipid Vesicle/Fluid Interactions in a Quasi–Newtonian Fluid Flow

We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in incompressible, non-Newtonian extracellular Carreau fluid. The membrane is captured with level set strategy. local inextensibility constraint relaxed introducing penalty which allows savings and facilitates implementation. A high-order Galerkin finite element approximation accurate calculations of derivatives. time discretization based on double composition one-step backward Euler scheme, while step size flexibly controlled using integration error estimation. Numerical examples are presented particular attention paid to validation assessment model’s relevance terms physiological significance. Optimal convergence rates obtained.