Solution of vector Stefan problems with cross-diffusion

Vermolen, F.J.; Vuik, C.

Solution of vector Stefan problems with cross-diffusion

Title

Solution of vector Stefan problems with cross-diffusion

Author

Vermolen, F.J.
Vuik, C.

Faculty

Electrical Engineering, Mathematics and Computer Science

Date

2003

Abstract

A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusant phase. To facilitate the analysis we use a diagonalization argument or Jordan factorization for the diffusion matrix. Self-similar solutions with the Boltzmann transformation are derived to get insight into qualitative behavior of the solution and for comparison with numerical solutions. Several numerical schemes for the solution of the Stefan problem are proposed and compared. It turns out that diagonalization is usefull for numerical purposes too. However, for the case of position dependent diffusion coefficients or a non diagonalizable diffusion matrix, one has to use a different scheme. Here, we analyze stability and workload of several time integrations.

Subject

multi-component alloy
particle dissolution
cross-diffusion
vector-valued Stefan problem
self-similar solution

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http://resolver.tudelft.nl/uuid:195781e7-e4f7-4127-9b49-301620b310c9

Publisher

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

ISSN

1389-6520

Source

Reports of the Department of Applied Mathematical Analysis, 03-14

Part of collection

Institutional Repository