Benchmarking of different strategies to include anisotropy in a curvature-driven multi-phase-field model

TL;DR

This paper develops and compares benchmark problems for assessing anisotropic curvature effects in phase field models, revealing that only one of three strategies reliably handles strong anisotropy.

Contribution

Introduces two benchmark problems for anisotropic curvature in phase field models and evaluates three methods of including anisotropy, identifying the most reliable approach for strong anisotropy.

Findings

One method reliably models strong anisotropy effects.

Benchmark problems effectively quantify shape and shrinkage accuracy.

Performance of inclusion strategies was comparable in initial tests.

Abstract

Two benchmark problems for quantitative assessment of anisotropic curvature driving force in phase field method were developed and introduced. Both benchmarks contained an anisotropically shrinking grain in homogeneous matrix. The first benchmark was a shrinking Wulff shape and in the second, such inclination dependence of the kinetic coefficient was added so that the shrinkage was isotropic. In both cases the match to the expected shape was quantified by means of Hausdorff distance and the shrinkage rate was analytically expressed. Three different ways of interface energy anisotropy inclusion in a multi-phase field model were compared. Because their performance was comparable, they were tested in an additional benchmark problem, which concerned direct measurement of equilibrium triple junction angles. Based on this benchmark, only one of the three strategies to include anisotropy was reliable in strongly anisotropic systems.