NUMERICAL RESOLUTION OF A PHASE CHANGE PROBLEM WITH ZERO LATENT HEAT

Abstract

Two numerical methods to simulate Ike behavior of a class offree-boundary thermal systems are presented and compared. The state of the system is governed by the conduction equation, where an isotherm defines the moving boundary for which a Neumann condition is considered. Unlike the classical Stefan problem, the moving boundary velocity does not appear explicitly in the heal balance

One method is based on the Friedman transformation and leads to a variational inequality defined on a fixed domain. Computation of the front velocity is not required

The other method uses the Landau transformation, leading to a new state equation of the convection-conduction type on a fixed domain. The convective part in the equation is due to the moving boundary. Estimation of the front velocity is obtained from the field temperature in the neighborhood of the boundary

The comparison between the two methods is performed on two examples—a freezing and a melting case—the exact solutions of which are known.