Universal Dynamics of Phase-Field Models for Dendritic Growth

TL;DR

This paper compares various phase-field models for dendritic growth, showing they produce identical results in the sharp interface limit and align with solvability theory, with no computational advantage for thermodynamically consistent models.

Contribution

It provides a comparative analysis of different phase-field models, highlighting their equivalence in the sharp interface limit and questioning the computational benefits of thermodynamic consistency.

Findings

Models agree in the sharp interface limit

Results match solvability theory

No computational advantage for thermodynamic models

Abstract

We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field equations are operating in their appropriate sharp interface limit. The long time steady state results are all in agreement with solvability theory. No computational advantage accrues from using a thermodynamically consistent phase-field model.