We present a fourth order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two dimensional convection diffusion equation. The seven point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth order convergence rate of the derived discretization scheme and to show that the fourth order compact difference scheme is computationally more efficient than the standard second order central difference scheme.

Mathematics Subject Classification: 65F10, 65N06, 65N22, 65N55, 76D07

Technical Report 341-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.