High accuracy benchmark problems for Allen-Cahn and Cahn-Hilliard dynamics
journal contribution
posted on 2023-06-09, 17:42authored byJon Matteo Church, Zhenlin Guo, Peter K Jimack, Anotida MadzvamuseAnotida Madzvamuse, Keith Promislow, Brian Wetton, Stephen M Wise, Fengwei Yang
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.
Funding
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION; 642866 - InCeM
EPSRC; EP/N007638/1
New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149