Second-order upwind differencing in a recirculating flow

In this study, we have investigated the accuracy and stability of the second-order upwind differencing scheme originally suggested by Price et al. and recently used by several others. The solution algorithm employed is based on a coupled solution of the nonlinear finite-difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite-difference grids. We observe that, in comparison with the hybrid differencing, the second-order upwind differencing is somewhat more accurate but that it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second-order upwind differencing.