Efficient linear, fully-decoupled and energy stable numerical scheme for a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field elastic bending energy model of lipid vesicles

Abstract

We first establish a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field variable elastic bending energy model for lipid vesicles, and then construct an efficient time-discrete scheme for solving it. The numerical scheme combines the penalty method for solving the Navier–Stokes equation, the explicit-IEQ (invariant energy quadratization) method for the nonlinear potentials, and the operator-splitting method. Hence it is not only fully decoupled but also owns some desired properties of linearity and unconditional energy stability. The feature of full decoupling is achieved by introducing some auxiliary variables and designing additional ordinary differential equations which are used for discretizing the coupled and nonlinear terms. The solvability and the unconditional energy stability of the numerical scheme have been further rigorously and numerically proven. Several numerical examples are carried out on the sedimentation process of the vesicle cell to show the effectiveness of the model and scheme.