Center for Computational Sciences
University of Kentucky
Lexington, KY 40506-0045, USA
Murli M. Gupta
Department of Mathematics
The George Washington University
Washington, DC 20052, USA
We present a fourth order compact finite difference scheme for a general three dimensional convection diffusion equation with variable coefficients on a uniform cubic grid. This high order compact difference scheme is used to solve convection diffusion equation with boundary layers on a three dimensional nonuniform grid. We compare the computed accuracy and computational efficiency of the fourth order compact difference scheme with that of the standard central difference scheme and the first order upwind difference scheme. Several convection diffusion problems are solved numerically to validate the proposed fourth order compact scheme.
Mathematics Subject Classification: 65M06, 65N12.