An Energy Stable C0 Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation

TL;DR

This paper introduces an energy-stable C0 finite element scheme for simulating vesicle motion and deformation using a phase-field model, ensuring thermodynamic consistency and numerical stability.

Contribution

It develops a second-order accurate finite element method for a thermodynamically consistent phase-field model of vesicle dynamics, incorporating slip boundary conditions.

Findings

The scheme is proven to be energy stable and mass-conserving.

Numerical tests confirm convergence and stability of the method.

Simulations illustrate effects of mechanical properties on vesicle behavior.

Abstract

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.