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A thermodynamically consistent phase-field model is introduced for simulatingmotion and shape transformation of vesicles under flow conditions. Inparticular, a general slip boundary condition is used to describe theinteraction between vesicles and the wall of the fluid domain. A second-orderaccurate in both space and time C0 finite element method is proposed to solvethe model governing equations. Various numerical tests confirm the convergence,energy stability, and conservation of mass and surface area of cells of theproposed scheme. Vesicles with different mechanical properties are also used toexplain the pathological risk for patients with sickle cell disease.

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