A new efficient fully-decoupled and second-order time-accurate scheme for Cahn–Hilliard phase-field model of three-phase incompressible flow
A new efficient fully-decoupled and second-order time-accurate scheme for Cahn–Hilliard phase-field model of three-phase incompressible flow
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DOI：
10.1016/j.cma.2020.113589
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发表时间：
2021-04
影响因子：
7.2
通讯作者：
Xiaofeng Yang
中科院分区：
文献类型：
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作者：
Xiaofeng Yang
对于三相不可压流的高耦合、非线性Cahn-Hilliard相场模型，如何建立具有二阶时间精度的全解耦数值格式一直是一个非常困难且尚未解决的问题。本文提出了一种新的解耦方法，该方法在每个时间步只需要求解几个解耦的常系数线性椭圆方程，就可以得到具有二阶时间精度的数值解。其核心思想是在系统中引入两个非局部辅助变量，其中一个用于线性化非线性势，另一个用于引入常微分方程来处理具有“零能量贡献”特性的非线性耦合项.我们严格证明了格式的可解性和无条件能量稳定性，并进行了二维和三维数值模拟，以显示格式的精度和稳定性。据作者所知，本文所发展的方法是流体力学耦合相场模型的第一个二阶全解耦格式。
For the highly coupled and nonlinear Cahn–Hilliard phase-field model of three-phase incompressible flow, how to establish a fully-decoupled numerical scheme with second-order time accuracy has always been a very difficult and unsolved problem. In this paper, we propose a novel decoupling method, which only needs to solve several decoupling linear elliptic equations with constant coefficients at each time step to obtain a numerical solution with second-order time accuracy. The key idea is to introduce two nonlocal auxiliary variables into the system, one of which is used to linearize the nonlinear potential, and the other is used to introduce an ordinary differential equation to deal with the nonlinear coupling terms with “zero-energy-contribution” characteristics. We strictly prove the solvability and unconditional energy stability of the scheme, and conduct numerical simulations in 2D and 3D to show the accuracy and stability of the scheme numerically. To the best of the author’s knowledge, the method developed in this paper is the first second-order fully-decoupled scheme for the hydrodynamics coupled phase-field model.