An analysis of solidification problems by the boundary element method

The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time‐dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time‐dependent Green's functions and convolution integrals. The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing. The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two‐dimensional problems. Comparison with existing semi‐analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.