Phase Field Models versus Parametric Front Tracking Methods: Are they accurate and computationally efficient?
This work provides a practical comparison for researchers choosing numerical methods for free boundary problems in materials science.
The paper compares phase field models and parametric front tracking methods for solidification problems, finding that parametric methods achieve higher accuracy with less computational cost for benchmark problems with exact solutions.
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.