A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between vesicles and
the wall of the fluid domain. A second-order accurate in both space and time C0 finite element method is proposed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patients with sickle cell disease.
In this paper, we focus on modeling and simulation of two-phase flow with moving contact lines and variable density. A thermodynamically consistent phase-field model with General Navier Boundary Condition is developed based on the concept of quasi-in
compressibility and the energy variational method. Then a mass conserving and energy stable C0 finite element scheme is developed to solve the PDE system. Various numerical simulation results show that the proposed schemes are mass conservative, energy stable and the 2nd order for P1 element and 3rd order for P2 element convergence rate in the sense of L2 norm.
