A High Order Compact Difference Scheme and Multigrid Method for Solving the 3D Convection Diffusion Equation on Non-uniform Grids

A high order compact (HOC) difference scheme is proposed to solve the 3D convection diffusion equation on non-uniform Cartesian grids involving no transformation from the physical space to the computational space. A multigrid method based on this HOC scheme is developed to solve the linear system arising from the difference equation. Numerical experiments about a boundary layer problem are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.