Two numerical methods for heat conduction problems with phase change

A fixed-space-step method and a fixed-time-step method are presented, respectively, for solving the Stefan problems with time-dependent boundary conditions. The evolution of the moving interface and the temperature distribution in the phase change domain are simulated numerically by using two methods for melting in the half-plane and outward spherical solidification. Numerical experiment results show that the numerical results obtained from the two methods are in good agreement for the different test examples, and the two methods can be applied to solve Stefan problems in engineering practice