Multicomponent diffusion simulation based on finite elements

A numerical model is presented to treat multicomponent, multiphase diffusion problems. Unlike other recent approaches that are based on the finite-difference method, analytical solutions, or particular thermodynamic models, a general procedure based on the finite-element technique is applied. The suggested formalism is based on the solution of the integral statement of the generalized diffusion equation. This treatment allows for a simple implementation of particular boundary conditions and can easily be extended from a one- to a multidimensional analysis. A brief overview of the formal representation of multicomponent diffusion coefficients, as suggested by Andersson and Agren, is given. The finite-element diffusivity matrices are evaluated for a one-dimensional bar and a two-dimensional triangular element. The model is applied to some classical examples in diffusion simulation in both one and two dimensions. The results are compared to available analytical solutions or experimental data.