A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters
A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters
复制标题
具有奇异界面参数的三元 Cahn-Hilliard 系统的保正性、能量稳定方案
DOI：
10.1016/j.jcp.2021.110451
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发表时间：
2021-06-08
影响因子：
4.1
通讯作者：
Zhang, Zhengru
中科院分区：
文献类型：
--
作者：
Dong, Lixiu;Wang, Cheng;Zhang, Zhengru
在本文中，我们为周期性三组分高分子微球复合（MMC）水凝胶系统（一个具有弗洛里 - 哈金斯 - 德热纳自由能势的三元Cahn - Hilliard系统）构建并分析了一种唯一可解、保持正性且无条件能量稳定的有限差分格式。所提出的格式基于对给定含两个变量的能量泛函的凸 - 凹分解，并且在空间上采用中心差分法。我们从理论上证明该数值格式有一对唯一解，使得所有奇异项始终保持正性，即不仅两个相变量始终在0到1之间，而且两个相变量之和在逐点意义上也在0到1之间。此外，我们使用局部牛顿近似和多重网格方法来求解这个非线性数值格式，并给出了各种数值结果，包括数值收敛性检验、正性保持性质检验、能量耗散和质量守恒性质。（C）2021爱思唯尔公司。保留所有权利。
In this paper, we construct and analyze a uniquely solvable, positivity preserving and unconditionally energy stable finite-difference scheme for the periodic three-component Macromolecular Microsphere Composite (MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy potential. The proposed scheme is based on a convex-concave decomposition of the given energy functional with two variables, and the centered difference method is adopted in space. We provide a theoretical justification that this numerical scheme has a pair of unique solutions, such that the positivity is always preserved for all the singular terms, i.e., not only two phase variables are always between 0 and 1, but also the sum of two phase variables is between 0 and 1, at a point-wise level. In addition, we use the local Newton approximation and multigrid method to solve this nonlinear numerical scheme, and various numerical results are presented, including the numerical convergence test, positivity-preserving property test, energy dissipation and mass conservation properties. (C) 2021 Elsevier Inc. All rights reserved.