Solution of vector Stefan problems with cross-diffusion

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 diffusive phase. Several numerical schemes for the solution of the Stefan problem are proposed and compared. It turns out that diagonalization is useful for numerical purposes. However, for the case of position-dependent diffusion coefficients one has to use a different scheme. Here, we analyze stability and workload of several time integration methods.