Numerical Method for One-Dimensional Phase Change Problems in Finite Regions

TLDR: In this article, the authors demonstrate the feasibility of a numerical technique to provide generalized solutions to one-dimensional phase change problems by using finite differences for a finite region undergoing one or more phase changes.

Abstract: An attempt is made to demonstrate the feasibility of a numerical technique to provide generalized solutions to one-dimensional phase change problems. In this simple and effective numerical method finite differences are used for a finite region undergoing one or more phase changes. The nonlinearity of the problem is isolated by a technique that accurately tracks the interfaces for all times. The temperatures away from the interfaces are obtained by using simple recurrence equations, thereby avoiding costly nodal iterations.