Diffuse interface models of solidification with convection: The choice of a finite interface thickness

TL;DR

This paper extends diffuse interface models of solidification to include convection, demonstrating that a thin interface limit is achievable with both diffusion and convection, validated by simulations and sharp-interface theory comparisons.

Contribution

It introduces a method to incorporate convection into thin interface limits of diffuse interface models, expanding their applicability.

Findings

Thin interface limit exists with convection included.

Simulation results agree with sharp-interface theory.

Method reduces numerical interface effects in solidification modeling.

Abstract

The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection.