A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

Authors:
Haiwei Sun;Ning Kang;Jun Zhang;Eric S. Carlson
Affiliations:
Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Department of Chemical Engineering, University of Alabama, P.O. Box 870203, Tuscaloosa, AL
Venue:
Mathematics and Computers in Simulation
Year:
2003

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Abstract

We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.