Fast implicit finite-difference method for the analysis of phase change problems

This paper develops a rapid implicit solution technique for the enthalpy formulation of conduction controlled phase change problems. Initially, three existing implicit enthalpy schemes are introduced. A new enthalpy solution scheme, requiring no under- or over-relaxation, is then developed. The previous three schemes and the new scheme are tested on a range of problems in one and two dimensions. A comparison of CPU times shows that the new scheme is between 1.5 and 10 times faster than the previous schemes.