A conserving discretization for a Stefan problem with an interface reaction at the free boundary
The dissolution of an $Al_2Cu$ particle is considered. A characteristic property is that initially the particle has a non-smooth boundary. Furthermore the dissolution may be controlled by an interface reaction. 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. We use the finite element method to solve this problem numerically. The displacement of the free boundary is computed by a method based on the balance of atoms. This method leads to good results, also for non-smooth boundaries. Some numerical experiments are given for the dissolution of an $Al_2Cu$ particle in an $Al$-$Cu$ alloy, with a varying rate of the interface reaction.
|Theoretical approximation to solutions (msc 35A35), Free boundary problems (msc 35R35), Finite difference methods (msc 65M06), Stefan problems, phase changes, etc. (msc 80A22)|
|Modelling, Analysis and Simulation [MAS]|
Vuik, C, Segal, G, & Vermolen, F.J. (1999). A conserving discretization for a Stefan problem with an interface reaction at the free boundary. Modelling, Analysis and Simulation [MAS]. CWI.