An Implicit Solution Procedure for Finite Difference Modeling of the Stefan Problem

A new procedure is presented for application to energy transport problems involving solid-to-liquid phase transition. The procedure is more implicit than previous solution procedures in an equation-solving sense and results in significantly lower computational costs. The method is formulated as a modified enthalpy model and is capable of solving problems for which many phase change interfaces exist simultaneously within the computational domain. The procedure is presented in a one-dimensional format but can be readily extended to multidimensional problems. Two rules which are reflections of the physical evolution are provided, are easily implemented, and form the basis of the new procedure. The procedure is demonstrated by application to several one-dimensional problems. Computational costs are compared to conventional procedures for a variety of boundary condition specifications, Stef an numbers, and mesh discretizations. The results indicate that a highly significant computational savings is realized with the new procedure, with cost reduction factors in excess of an order of magnitude.