Phase Field Models versus Parametric Front Tracking Methods: Are they accurate and computationally efficient?

TL;DR

This paper compares phase field models and parametric front tracking methods in terms of accuracy and computational efficiency for solidification problems, especially Stefan problems, using benchmark tests and new discretization techniques.

Contribution

It introduces high-quality mesh parametric methods and stable discretizations for phase field models, providing a comprehensive comparison with sharp interface approaches.

Findings

Parametric methods achieve high mesh quality.

New discretizations improve phase field stability.

Benchmark results highlight differences in accuracy and efficiency.

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.