NUMERICAL SOLUTION OF THE INVISCID STAGNATION-FLOW SOLIDIFICATION PROBLEM

Abstract

The inviscid stagnation-flow solidification problem is investigated by applying the finite difference method after a coordinate transformation to a fixed domain. Numerical solutions of the temperature distribution and the solid-liquid interface location as well as its growth rate are obtained, and comparisons with the instantaneous-similarity solution and the quasi-steady solution are made. Since the transformed system of equations for this solidification problem has a singularity at t = 0, the finite difference solution is started at a small time using the instantaneous-similarity solution as the initial field. The numerical solution confirms the existence of an asymptotic limit of the solidification front as previously demonstrated by means of both a quasi-steady and an instantaneous-similarity solution.