G. Segal et al., A CONSERVING DISCRETIZATION FOR THE FREE-BOUNDARY IN A 2-DIMENSIONAL STEFAN PROBLEM, Journal of computational physics, 141(1), 1998, pp. 1-21
The dissolution of a disk-like Al2Cu particle is considered. A charact
eristic property is that initially the particle has a nonsmooth bounda
ry. The mathematical model of this dissolution process contains a desc
ription of the particle interface, of which the position varies in tim
e. 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 u
nrealistic. 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 experimen
ts are given for the dissolution of an Al2Cu particle in an AI-Cu allo
y. (C) 1998 Academic Press.