Efficient computation of a sharp interface by spreading via phase field methods

Abstract

A sharp interface arising from any of the major transition problems (calssical or modified stefan, etc.) can be smoothed out using the phase field approach as a numerical tool. The computations in one-dimensional space and n-dimensions with radial symmetry indicate that this efficient method for dealing with stiff equations results in a very accurate interface determination without explicit tracking. The methods also provide a numerical verification of the concept of a critical radius.