An alternative fixed grid method for solution of the classical one-phase Stefan problem

Abstract

In this paper, an alternative fixed grid method based on explicit finite difference technique has been presented to solve the classical one-phase Stefan problem. The most popular fixed grid method developed by Murray and Landis, which utilises fictitious temperature for the grid containing the fusion front, has been revisited. The concept of a fictitious temperature for the grid-containing interface, as proposed by Murray and Landis, has been eliminated and an alternative equation has been developed for the energy balance of grid point neighbouring the interface. Identical results have been obtained by the alternative fixed-grid and by the Murray–Landis fixed-grid method. Though the paper deals with explicit finite difference schemes only, the alternative method can also be applied to implicit formulation for one-phase as well as two-phase moving boundary problems.