Sharp phase-field modeling of isotropic solidification with a super efficient spatial resolution

TL;DR

This paper introduces a local translational invariance restoration scheme in phase-field models, enabling efficient and isotropic solidification simulations at minimal spatial resolution, overcoming previous grid-related limitations.

Contribution

It proposes a novel local TI restoration method that accurately models isotropic solidification with one-grid-point resolution, reducing grid anisotropy effects.

Findings

Successfully captures isotropic seaweed structures without grid-induced artifacts.

Enables high-fidelity solidification modeling at minimal spatial resolution.

Overcomes limitations of previous global TI approaches.

Abstract

The numerical resolution efficiency of phase-field models is limited by grid friction, grid anisotropy and pinning. The 1D sharp phase-field model eliminates grid friction and pinning by a global restoration of Translational Invariance (TI) in the discretized phase-field equation (Phys. Rev. Lett. 121, 025501, 2018). In 3D global TI restricts the beneficial modeling properties to a finite number of fixed interface orientations. We propose an accurate scheme to restore TI locally in the local interface normal direction. At one-grid-point interface resolutions, the new model captures the formation of isotropic seaweed structures without spurious dendritic selection by grid anisotropy.