Computation of sharp phase boundaries by spreading: The planar and spherically symmetric cases

Abstract

The sharp interface that arises from any of the major transition problems (classical or modified Stefan, etc.) can be smoothed using the phase field approach as a numerical tool. The basic idea is that the thickness of the interface can be regarded as a mathematical free parameter which can be stretched beyond its physical value for computational convenience. The computations in one dimensional space and n dimensions with radial symmetry indicate that this is an efficient method for dealing with stiff equations and results in a very accurate interface determination without explicit tracking. The question of optimizing the interfacial thickness with respect to grid size is also considered empirically. The technique also provides a numerical verification of the concept of an unstable critical radius of solidification