A comparison of numerical models for one-dimensional Stefan problems

In this paper we present a critical comparison of the suitability of several numerical methods, level set, moving grid and phase eld model, to address two well known Stefan problems in phase transformation studies: melting of a pure phase and diusional solid state phase transformations in a binary system. Similarity solutions are applied to...

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 diffusant phase. To facilitate the analysis we use a...

Mathematical models for particle dissolution in metallic alloys

This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in...

Deflation in preconditioned conjugate gradient methods for Finite Element Problems

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous coefficients that vary in several orders of...

A mathematical model for the dissolution of stoichiometric particles in multi-component alloys

A general model for the dissolution of stoichiometric particles in multi-component alloys is proposed and analysed. We introduce the concept of mass-conserving solutions and give a self-similar solution for the resulting Stefan-problem. Furthermore, we show that particle dissolution in multi-component alloys can under certain circumstances be...

Some mathematical aspects of particle dissolution and cross-diffusion in multi-component alloys

A general model for the dissolution of stoichiometric particles, taking into account the influences of cross-diffusion, in multi-component alloys is proposed and analyzed using a diagonalisation argument. We give a self-similar solution for the resulting Stefanproblem and state when the solutions are mass-conserving. We also give criteria for...

The influence of deflation vectors at interfaces on the deflated conjugate gradient method

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods. Our set-up is a Laplace problem in two dimensions with continuous or discontinuous coeffcients that vary in several orders of magnitude. In the continuous case we are interested in the convergence...

A numerical analysis for the dissolution of second phase particles in ternary alloys