Ak. Verma et V. Eswaran, OVERLAPPING CONTROL-VOLUME APPROACH FOR CONVECTION-DIFFUSION PROBLEMS, International journal for numerical methods in fluids, 23(9), 1996, pp. 865-882
This paper introduces a finite volume method to solve 2D steady state
convection-diffusion problems on structured non-orthogonal grids. Over
lapping control volumes (OCV) are used to discretize the physical doma
in and the governing equations are solved without transformation. An i
soparametric formulation is used to compute diffusion and for upwindin
g. Four test problems are solved using this and other schemes. The mod
elling of diffusion in OCV seems very effective even on distorted mesh
es. The convection modelling in OCV is found to be sec end-order-accur
ate, like QUICK, on regular meshes. Although its accuracy is slightly
inferior to the latter on rectangular grids, its faster convergence gi
ves it a better overall performance. On non-orthogonal grids, OCV give
s better accuracy for a large and practical range of Peclet numbers th
an does QUICK applied to the transformed equations using the conventio
nal five-point diffusion modelling. The results obtained also demonstr
ate that the scheme reduces false diffusion to a considerable extent i
n comparison with the power-law scheme.