A new numerical approach to the two-dimensional Stefan problem

A new approach to the two-dimensional Stefan problem is presented in the paper. In contrast to other methods, special attention is paid to finding the velocity of its moving interface so as to obtain phase-change domain. Meanwhile, a special mesh generation technique is suggested. The proposed method requires no iteration to determine the moving front, leading to a very simple numerical procedure even for complicated boundary conditions. Some examples are given, revealing its effectiveness and convenience.