Numerical treatment of diffusion coefficients at interfaces

The main purpose of this work is to evaluate the values of diffusion coefficients at control- volume faces, using the finite-volume method, in transport problems that include diffusion processes. A heat conduction problem in a composite slab with linearly temperature- dependent conductivity, which has a closed-form solution, is selected for demonstration. It is found that the harmonic mean operation performs better than the arithmetic mean operation in evaluating the interface diffusion coefficients. Moreover, if we intend to obtain the information at some specific interfaces with abrupt changes of diffusion coefficients, the recommended grid layout is arranged such that each specific interface contains a grid node. This arrangement can give more accurate predictions at these unusual interfaces.