Phase Field Models versus Parametric Front Tracking Methods: Are they accurate and computationally efficient?
arXiv:1212.2077 · doi:10.4208/cicp.190313.010813a
Abstract
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Particular emphasis is put on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.
51 pages, 22 figures, 15 tables
References in corpus (4)
- Numerical computations of facetted pattern formation in snow crystal growth
- Stable Phase Field Approximations of Anisotropic Solidification
- On the stable discretization of strongly anisotropic phase field models with applications to crystal growth
- Finite-Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law