Precise time-domain expanding boundary element method for solving phase change problems

In this article, the precise time-domain expanding boundary element method (PTEBEM) is applied to solving phase change problems. In the present method, the recursive formulation of the governing equation is derived by expanding time-dependent physical quantities at discrete time intervals. Then the recursive equation is solved by the radial integration boundary element method, where the radial integral method is used to transform the domain integral into the boundary integral. Moreover, in order to guarantee the accuracy and efficiency, a self-adaptive check scheme is introduced to evaluate the recursive times in a time step. Simultaneously, the front-tracking method is used to simulate the motion of the moving boundary. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing PTEBEM. To verify the present method, several typical examples are given. Satisfactory results are obtained in comparison with reference solutions.