Accuracy, Robustness, and Efficiency Comparison in Iterative
Computation of Convection Diffusion Equation with Boundary Layers

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

Abstract

Nine point fourth order compact finite difference scheme, central difference scheme, and upwind difference scheme are compared for solving the two dimensional convection diffusion equations with boundary layers. The domain is discretized with a stretched nonuniform grid. A grid transformation technique maps the nonuniform grid to a uniform one, on which the difference schemes are applied. A multigrid method and a multilevel preconditioning technique are used to solve the resulting sparse linear systems. We compare the accuracy of the computed solutions from different discretization schemes, and demonstrate the relative efficiency of each scheme. Comparisons of maximum absolute errors, iteration counts, CPU timings, and memory cost are made with respect to the two solution strategies.


Key words: convection diffusion equation, boundary layer, grid stretching, multilevel preconditioner, multigrid method


This paper has been published in Numerical Methods for Partial Differential Equations, Vol. 16 (4), 379-394 (1000).
It was also published as Technical Report No. 291-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999.
This research was supported in part by the National Science Foundation under grant CCR-9902022, in part by the University of Kentucky Center for Computational Sciences, and in part by the University of Kentucky College of Engineering.