Accuracy, robustness, and efficiency comparison in iterative computation of convection diffusion equation with boundary layers

Nine-point fourth-order compact finite difference scheme, central difference scheme, and upwind difference scheme are compared for solving the two-dimensional convection diffusion equations with boundary layers. The domain is discretized with a stretched nonuniform grid. A grid transformation technique maps the nonuniform grid to a uniform one, on which the difference schemes are applied. A multigrid method and a multilevel preconditioning technique are used to solve the resulting sparse linear systems. We compare the accuracy of the computed solutions from different discretization schemes, and demonstrate the relative efficiency of each scheme. Comparisons of maximum absolute errors, iteration counts, CPU timings, and memory cost are made with respect to the two solution strategies.