An optimal weighted upwinding covolume method on non-standard grids for convection-diffusion problems in 2D

In this paper we develop an optimal weighted upwinding covolume method on non-standard covolume grids for convection–diffusion problems in two dimensions. The novel feature of our method is that we construct the non-standard covolume grid in which the nodes of covolumes vary in the interior of different volumes of primary grid depending on the local weighted factors and further on the local Peclet’s numbers. A simple method of finding the local optimal weighted factors is also derived from a non-linear function of local Peclet’s numbers. The developed method leads to a totally new scheme for convection–diffusion problems, which overcomes numerical oscillation, avoids numerical dispersion, and has high-order accuracy. Some theoretical analyses are given and numerical experiments are presented to illustrate the performance of the method