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Volume 26, Issue 4
High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

Jon Matteo Church, Zhenlin Guo, Peter K. Jimack, Anotida Madzvamuse, Keith Promislow, Brian Wetton, Steven M. Wise & Fengwei Yang

DOI: 10.4208/cicp.OA-2019-0006

Commun. Comput. Phys., 26 (2019), pp. 947-972.

Published online: 2019-07

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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 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.

  • Keywords

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

  • AMS Subject Headings

65M06, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

j.m.church@leeds.ac.uk (Jon Matteo Church)

zhenling@math.uci.edu (Zhenlin Guo)

p.k.jimack@leeds.ac.uk (Peter K. Jimack)

A.Madzvamuse@sussex.ac.uk (Anotida Madzvamuse)

kpromisl@math.msu.edu (Keith Promislow)

wetton@math.ubc.ca (Brian Wetton)

swise1@utk.edu (Steven M. Wise)

fengwei.yang@surrey.ac.uk (Fengwei Yang)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-26-947, author = {Church , Jon MatteoGuo , ZhenlinJimack , Peter K.Madzvamuse , AnotidaPromislow , KeithWetton , BrianM. Wise , Steven and Yang , Fengwei}, title = {High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {4}, pages = {947--972}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0006}, url = {http://global-sci.org/intro/article_detail/cicp/13225.html} }
TY - JOUR T1 - High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics AU - Church , Jon Matteo AU - Guo , Zhenlin AU - Jimack , Peter K. AU - Madzvamuse , Anotida AU - Promislow , Keith AU - Wetton , Brian AU - M. Wise , Steven AU - Yang , Fengwei JO - Communications in Computational Physics VL - 4 SP - 947 EP - 972 PY - 2019 DA - 2019/07 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2019-0006 UR - https://global-sci.org/intro/article_detail/cicp/13225.html KW - Allen-Cahn, Cahn-Hilliard, phase field, benchmark computation. AB -

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.

Church , Jon MatteoGuo , ZhenlinJimack , Peter K.Madzvamuse , AnotidaPromislow , KeithWetton , BrianM. Wise , Steven and Yang , Fengwei. (2019). High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics. Communications in Computational Physics. 26 (4). 947-972. doi:10.4208/cicp.OA-2019-0006
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