Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
A numerical method to compute the dissolution of second phases in ternary alloys
Journal of Computational and Applied Mathematics
A mathematical model for the dissolution of particles in multi-component alloys
Journal of Computational and Applied Mathematics
Cross-diffusion controlled particle dissolution in metallic alloys
Computing and Visualization in Science
Journal of Computational Physics
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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.