Numerical Method for Multi-Dimensional Freezing Problems in Arbitrary Domains

This paper presents a simple numerical method for solving two and three-dimensional freezing problems with arbitrary geometries. The change of variable method introduced by Landau for the one-dimensional problem is extended to the multi-dimensional using an independent variable which takes constant values at the boundary and the freezing front. Example calculations were performed for the Stefan type freezing problem in regular squares, triangles, and ellipses. Then some of the results were compared with the experimental ones that were obtained for the constant cooling rate.