A Fixed-Grid Finite-Difference Method for Solidification Problems

Abstract

For a numerical solution of solidification problems, a fixed-grid finite-difference method is a popular approach due to the ease of its implementation and less computational effort than the moving-grid system. However, the simple discretisation of the fixed-grid method has a tendency to osdllate numerically in temperature and solid-liquid interface position. The numerical oscillations arise from improper handling of the evolution of the latent heat at the solid-liquid interface. In this work, a modified discretisation is described such that the numerical error could be overcome. A onedimensional solidification problem with known analytical solution is applied to demonstrate the efficiency of the method.