Grid for Two Dimensional Convection-Diffusion Equation

Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

773 Anderson Hall

Lexington, KY 40506-0046, USA

Jules Kouatchou

Morgan State University

School of Engineering

Baltimore, MD 21239, USA

and

Lixin Ge

Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

773 Anderson Hall

Lexington, KY 40506-0046, USA

We derive a family of fourth order finite difference schemes on the rotated grid for the two dimensional convection diffusion equation with variable coefficients. In the case of constant convection coefficients, we present an analytic bound on the spectral radius of the line Jacobi iteration matrix in terms of the cell Reynolds numbers. Our analysis and numerical experiments show that the proposed schemes are stable and produce highly accurate solutions. Classical iterative methods with these schemes are convergent with large values of the convection coefficients. We also compare the fourth order schemes with the nine point scheme obtained from the second order central difference scheme after one step of cyclic reduction.

Key words: convection diffusion equation, rotated grid, fourth order difference schemes.

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This paper has been published in

Technical Report No. 310-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000. This research was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165 and CCR-0043861, and in part by NASA under grant No. NAGS-3508.