Construction of effective computational algorithms for solving free boundary problems

Abstract

An efficient method for numerically solving the one-dimensional Stefan problem is proposed herein. A computational algorithm for solving free boundary problems has been developed. This provides a means of solving problems with an arbitrary and variable number of phases, both in terms of thermal conductivity and diffusion. The solution algorithm is based on the application of the finite element method. The calculations are performed according to a homogeneous scheme. This makes the method universal and renders it possible to be referred to the class of shock-capturing methods. Accurate tracking of the position of the boundaries is carried out, in the same manner as in the methods with edge detection, which makes it possible to solve problems with high accuracy, inherent in methods of this type.