Abstract: In this paper the Boundary element Method (BEM) is Successfully applied to the three-dimensional numerical Simulation of the directional solidification (DS) Process in the steady state, and a lot of information about the process is obtained. The effect of non-linear thermal conductivity and non-linear heat transfer coefficient under different boundary conditions is investigated. The results show that in certain conditions the non-linear parameters can be simplified, and thus a large scale numerical simulation for the real DS process in engineering is possible on a microcomputer.

Key words: numerical simulaton, directional solidification in steady state, gcastings