A conserving discretization for a Stefan problem with an interface reaction at the free boundary

Abstract

The dissolution of an Al 2 Cu 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 2 Cu particle in an Al-Cu alloy, with a varying rate of the interface reaction.1991 Mathematics Subject Classification: 35A35, 35R35, 65M06, 80A22

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