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

Authors

  • Jon Matteo Church School of Computing, University of Leeds, Leeds, LS2 9JT, United Kingdom.
  • Zhenlin Guo Mathematics Department, UC Irvine, Irvine, 92697-3875, USA.
  • Peter K. Jimack
  • Anotida Madzvamuse University of Sussex, Brighton, BN1 9RH, United Kingdom.
  • Keith Promislow Department of Mathematics, Michigan State, East Lansing, 48864, USA.
  • Brian Wetton Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
  • Steven M. Wise Department of Mathematics, University of Tennessee, Knoxville, 37996-1320, USA.
  • Fengwei Yang Department of Chemical and Process Engineering, University of Surrey, Stag Hill Campus, Guildford, Surrey, GU2 7XS, United Kingdom.

DOI:

https://doi.org/10.4208/cicp.OA-2019-0006

Keywords:

Allen-Cahn, Cahn-Hilliard, phase field, benchmark computation.

Abstract

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.

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Published

2019-07-02

Issue

Vol. 26 No. 4 (2019)

Section

Articles