Numerical analysis with the phase field equations for the Stefan problems

TL;DR

This paper presents a numerical approach using phase field equations to analyze Stefan problems in two dimensions, effectively tracking interface movements without relying on velocity functions like Navier-Stokes.

Contribution

It introduces a novel numerical method employing phase field equations to model Stefan problems, avoiding the need for unknown velocity functions.

Findings

Successfully modeled interface dynamics in two dimensions

Demonstrated effectiveness in dissolution and precipitation scenarios

Provided a new computational framework for Stefan problems

Abstract

Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which complicated movements or changes are needed. More precisely, we analyze the dissolution and/or precipitation without the unknown velocity functions like the Navier-Stokes equations numerically.