A fixed-grid finite-difference method for phase-change problems

Abstract

A simple finite-difference method was developed for solid-liquid phase-change problems. The present method is based on a fixed grid and implicit in time. A fictitious temperature concept is introduced to derive finite-difference equations to deal with the nodal points across the solid-liquid interface, The algorithm is applied to a one-dimensional Stefan problem for which exact solutions ave available. The computational results ave found to be in excellent agreement with the exact solutions, Further, the present method yields no oscillations of temperature and phase front, which ave commonly observed with the typical enthalpy method.