High accuracy benchmark problems for Allen-Cahn and Cahn-Hilliard dynamics

Church, Jon Matteo, Guo, Zhenlin, Jimack, Peter K, Madzvamuse, Anotida, Promislow, Keith, Wetton, Brian, Wise, Stephen M and Yang, Fengwei High accuracy benchmark problems for Allen-Cahn and Cahn-Hilliard dynamics. Communications in Computational Physics, 26 (4). pp. 947-972. ISSN 1815-2406 (Accepted)

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Abstract

There is a large literature of numerical methods for phase field models from materials science. The prototype models are the AllenCahn 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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematics Applied to Biology Research Group
Subjects: Q Science
Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 07 May 2019 10:01
Last Modified: 03 Jul 2019 12:15
URI: http://sro.sussex.ac.uk/id/eprint/83518

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EPSRCUnsetUnsetEP/N007638/1
Unravelling new mathematics for 3D cell migrationG1438LEVERHULME TRUSTRPG-2014-149