A Sharp Phase Field Method

TL;DR

This paper introduces a novel phase field method that discretizes interfaces with high accuracy using minimal grid points, enhancing computational efficiency and rotational invariance for microstructural evolution simulations.

Contribution

A new intrinsically discrete phase field formulation that accurately resolves interfaces with minimal grid points and improved rotational invariance.

Findings

Interfaces are resolved with essentially one grid point.

High accuracy in reproducing interfacial kinetic properties.

Effective coupling of conserved and non-conserved fields.

Abstract

Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve the continuous character of the theory. We present here a new formulation, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method. We show that interfacial kinetic properties are reproduced with a high accuracy. Finally, we apply the model to a situation where conserved and non-conserved fields are coupled.