A numerical model was presented for the treatment of multi-component multi-phase diffusion problems. A general procedure which was based upon the finite-element technique was used, rather than one which was based upon the finite-difference method, analytical solutions or particular thermodynamic models. The present formalism was based upon the solution of the integral form of the generalized diffusion equation. This treatment permitted the simple incorporation of particular boundary conditions, and could be easily extended from a 1-dimensional to a multi-dimensional analysis. A brief review of the formal representation of multi-component diffusion coefficients was presented. The finite-element diffusivity matrices were evaluated for a 1-dimensional bar and for a 2-dimensional triangular element. The model was applied to classical examples of diffusion simulation in 1 and 2 dimensions.

Multicomponent Diffusion Simulation Based on Finite Elements. E.Kozeschnik: Metallurgical and Materials Transactions A, 1999, 30[10], 2575-82