High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

被引：43

作者：

Church, Jon Matteo ^{[1
]}

Guo, Zhenlin ^{[2
]}

Jimack, Peter K. ^{[1
]}

Madzvamuse, Anotida ^{[3
]}

Promislow, Keith ^{[4
]}

Wetton, Brian ^{[5
]}

Wise, Steven M. ^{[6
]}

Yang, Fengwei ^{[7
]}

机构：

[1] Univ Leeds, Sch Comp, Leeds LS2 9JT, W Yorkshire, England

[2] UC Irvine, Math Dept, Irvine, CA 92697 USA

[3] Univ Sussex, Brighton BN1 9RH, E Sussex, England

[4] Dept Math, E Lansing, MI 48864 USA

[5] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[6] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[7] Univ Surrey, Dept Chem & Proc Engn, Stag Hill Campus, Guildford GU2 7XS, Surrey, England

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2019年 / 26卷 / 04期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

Allen-Cahn; Cahn-Hilliard; phase field; benchmark computation; FINITE-DIFFERENCE; ENERGY; CONVERGENCE; EQUATIONS; SCHEMES; MODELS; SYSTEM; FLOWS;

D O I：

10.4208/cicp.OA-2019-0006

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

There is a large literature of numerical methods for phase field models from materials science. The prototype models are the Allen-Cahn and Cahn-Hilliard equations. We present four benchmark problems for these equations, with numerical results validated using several computational methods with different spatial and temporal discretizations. Our goal is to provide the scientific community with a reliable reference point for assessing the accuracy and reliability of future software for this important class of problem.

引用

页码：947 / 972

页数：26

共 49 条

[1] CONVERGENCE OF THE CAHN-HILLIARD EQUATION TO THE HELE-SHAW MODEL [J].