Abstract
We propose a high order alternating direction implicit (ADI) solution method for solving unsteady convection-diffusion problems. The method is fourth order in space and second order in time. It permits multiple use of the one-dimensional tridiagonal algorithm with a considerable saving in computing time, and produces a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable for 2D problems. Numerical experiments are conducted to test its high accuracy and to compare it with the standard second-order Peaceman-Rachford ADI method and the spatial third-order compact scheme of Noye and Tan.
| Original language | English |
|---|---|
| Pages (from-to) | 1-9 |
| Number of pages | 9 |
| Journal | Journal of Computational Physics |
| Volume | 198 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 20 2004 |
Bibliographical note
Funding Information:The research work of the authors was supported in part by the US National Science Foundation under Grants CCR-9988165, CCR-0092532, ACR-0202934, and ACR-0234270, in part by the US Department of Energy Office of Science under Grant DE-FG02-02ER45961, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-02-264-RED-002, in part by the Japan Research Organization for Information Science and Technology (RIST).
Keywords
- ADI method
- High order compact scheme
- Stability
- Unsteady convection-diffusion equation
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics