Abstract
We derive a high-order compact alternating direction implicit (ADI) method for solving three-dimentional unsteady convection-diffusion problems. The method is fourth-order in space and second-order in time. It permits multiple uses of the one-dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second-order Douglas-Gunn ADI method and the spatial fourth-order compact scheme by Karaa.
| Original language | English |
|---|---|
| Pages (from-to) | 983-993 |
| Number of pages | 11 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 22 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jul 2006 |
Keywords
- ADI method
- High-order compact scheme
- Stability
- Unsteady convection-diffusion problem
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics