Numerical approximations of the Navier-Stokes equation coupled with volume-conserved multi-phase-field vesicles system: Fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme

摘要

We consider the numerical approximation of the flow-coupled multi-phase-field elastic bending energy model of lipid vesicles. Based on the classical model with approximate volume conservation only, this paper first establishes a new model that can accurately conserve volume by adding some nonlocal terms to the model equation. Then, for the system coupled with the incompressible flow, we propose a novel numerical method to construct an effective scheme that is fully-decoupled, linear, unconditionally energy stable, and second-order time-accurate. The key idea to achieve the full decoupling nature is to introduce an ordinary differential equation to deal with the nonlinear coupling term that satisfies the so-called "zero-energy-contribution" property. Thus, in actual calculations, this scheme only needs to solve several independent linear equations with constant coefficients at each time step. We strictly prove the solvability and unconditional energy stability, and perform numerical simulations in 2D and 3D to verify the accuracy and stability of the scheme numerically. (C) 2020 Elsevier B.V. All rights reserved.