A conserving discretization for the free boundary in a two-dimensional Stefan problem

The dissolution of a disk-like Al2Cu particle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms, This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of an Al2Cu particle in an AI-Cu alloy. (C) 1998 Academic Press.