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
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
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.