Stability Analysis of Solution Methods for a Phase Transition Problem

Abstract

We consider a model of crystallization process in a binary compound taking into account heat and mass transfer in the solid and liquid phases. Stability of various methods for the numerical implementation of nonlinear conditions on a moving internal boundary is analyzed. For a group of methods based on the successive solution of governing equations, the stability domains determined by the system thermodynamic parameters are indicated. A coupled algorithm for solving the problem is proposed. Nonlinear equations at the phase interface are solved by the Newton method. The coupled algorithm has a significant stability margin and provides reliable results in a broad range of parameters of practical interest.