Second-order upwind and central difference schemes for recirculatingflow computation

Abstract

Two-dimensional driven cavity flows with the Reynolds number ranging from 102 to 3.2×103 are used to assess the performance of second-order upwind and central difference schemes for the convection terms. Three different implementations of the second-order upwind scheme are designed and tested in the context of the SIMPLE algorithm, with the grid size varying from 21×21 to 161×161 uniformly spaced nodes. Converged solutions are obtained for all Reynolds numbers. Although these different implementations of the second-order upwind scheme have the same formal order of accuracy, significant differences in numerical accuracy are observed. It is demonstrated that better performance can be obtained for the second-order upwind scheme if the discretization is cast in accordance with the finite volume formulation. Although both the second-order upwind and central difference schemes exhibit no oscillations in the solution, the upwind scheme is more accurate. In assessing and comparing the performance of these schemes, the distribution of cell Reynolds number is discussed and its impact on numerical accuracy illustrated