Abstract: In this paper,a new boundary ingegral equation scheme is presented for the solution of some two-dimensional phase change problems. Using weighted residual technique,a general formulation based on space-time Green's functions is developed. Then a descritized system is-constructed,featuring quadratic interpolation over space and linear interpolation over time. The time-dependent fundamental solution is introduced together with its time and boundary inge-gration treatment. Several typical numerical examples are included to demonstrate the accuracy and stability of the numerical BEM model.

Key words: Phase change problems, Boundary element method (BEM), Time-dependent fundamental solution