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.
| Original language | English |
|---|---|
| Pages (from-to) | 651-661 |
| Number of pages | 11 |
| Journal | Mathematics and Computers in Simulation |
| Volume | 63 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 24 2003 |
Bibliographical note
Funding Information:The research work of the authors was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, ACR-0202934, in part by the US Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology (RIST), and in part by the University of Kentucky Research Committee.
Keywords
- Convection diffusion equation
- Face centered cubic grid
- Fourth-order compact scheme
- Multigrid method
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics