Solving phase change problems via a precise time-domain expanding boundary element method combined with the level set method

Abstract

Phase change problems are investigated numerically in this study. A combined precise time-domain expanding boundary element method (PTEBEM) and the level set method is proposed. The PTEBEM is employed on one hand to solve the temporal-spatial field partial differential equations of the transient heat transfer problem. The radial integral method is used to transform the domain integral of the governing equation into a boundary integral. On the other hand, the level set method which is widely used to track crack trajectories is here employed to handle the complicated topological changing during phase change, to record the position of material phase interface during moving, merging or slipping. The formed numerical framework is further enhanced for higher stability. To demonstrate the accuracy and robustness of the proposed method, a few examples are provided.