On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Abstract

Explicit numerical schemes obtained using variable space grid (VSGM) and boundary immobilization (BIM) methods are considered for the solution of the transient heat conduction problem with phase change. This article briefly reviews different approaches developed to track the phase change front with a particular interest to those tracking explicitly the moving boundary. The analysis shows that both methods lead to identical computational algorithm, then considers the modified numerical scheme developed by Kutluay et al. (J. Comput. Appl. Math. 81 (1997) 135–144) and proposes a refinement procedure for the scheme without any additional CPU time. Two Stefan-like problems, having exact solutions, are studied and numerical results are assessed with respect to their performances.