Fourth Order Compact Difference Scheme for 3D Convection
Diffusion Equation with Boundary Layers on Nonuniform Grids

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Lexin Ge
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.

Key words: convection diffusion equation, boundary layer, grid stretching, fourth order compact scheme.

Mathematics Subject Classification: 65M06, 65N12.

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This paper has been published in Neural, Parallel & Scientific Computations, Volume 8, Number 3 & 4, pages 373-392, 2000. Also as Technical Report 298-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences.