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 - <p style="text-align: justify;">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.</p>