A practical and efficient numerical method for the Cahn-Hilliard equation in complex domains

被引：24

作者：

Jeong, Darae ^{[1
]}

Yang, Junxiang ^{[2
]}

Kim, Junseok ^{[2
]}

机构：

[1] Kangwon Natl Univ, Dept Math, Chunchon 24341, Gangwon Do, South Korea

[2] Korea Univ, Dept Math, Seoul 02841, South Korea

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 73卷

基金：

新加坡国家研究基金会;

关键词：

Ternary Cahn-Hilliard system; Cahn-Hilliard equation; Complex domain; Phase separation; Multigrid method; FINITE-ELEMENT-METHOD; FOURIER-SPECTRAL METHODS; ISOGEOMETRIC ANALYSIS; BOUNDARY-CONDITIONS; 2-PHASE FLOW; MODELS; CONVERGENCE; SYSTEMS; SCHEME;

D O I：

10.1016/j.cnsns.2019.02.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we present a practical and efficient numerical method for the Cahn-Hilliard (CH) equation in the two-and three-dimensional complex domains. We propose a simple mathematical model for the binary mixture in the complex domains. The model is based on the ternary CH system. An arbitrary domain is represented by the third phase, which is fixed during the temporal evolution of the other phases. By the local conservative property of the sum of the phases, the governing equation is simplified to a binary CH equation with a source term. For the numerical solution, we use a practically unconditionally gradient stable scheme. Various numerical experiments are performed on arbitrary domains. The numerical results show that the proposed algorithm can deal with the complex domains efficiently. (c) 2019 Elsevier B.V. All rights reserved.

引用

页码：217 / 228

页数：12

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