High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

A fourth-order compact finite difference scheme and a multigrid method are employed to solve the two-dimensional convection diffusion equations with boundary layers. The computational domain is first discretized on a nonuniform (stretched) grid to resolve the boundary layers. A grid transformation technique is used to map the nonuniform grid to a uniform one. The fourth-order compact scheme is applied to the transformed uniform grid. A multigrid method is used to solve the resulting linear system. Numerical experiments are used to show that a graded mesh and a grid transformation are necessary to compute high accuracy solutions for the convection diffusion problems with boundary layers and dicretized by the fourth-order compact scheme.