REMARKS ON THE PHYSICAL BASIS FOR THE CONSTRUCTION OF DIFFUSION FLUX TERMS IN FINITE-VOLUME EQUATIONS

Abstract

The formulation for the diffusion terms in unstructured meshes is compared to that previously derived by the present authors and others for structured body-fitted meshes in terms of direction cosines between the normal and tangential directions. The so-called 'over-relaxed' approach is entirely equivalent/identical, subject to the caveat that the gradient of a scalar field is computed as the product of the scalar and the local surface area vector per unit volume summed (integrated) over the cell volumes, rather than by bilinear field interpolation. The physical/mathematical basis for the 'minimum correction' and 'orthogonal correction' approaches is not consistent with the present authors' derivation, which is in agreement with previous observations. The derivation for a structured mesh here differs from previous work in that physical, rather than mathematical components/projections of vectors are considered, thus filling a significant historical gap in the literature.