High Order ADI Method For Solving Unsteady Convection-Diffusion Problems

Samir Karaa, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA


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 2-D problems and it is easily extendible to higher dimensional 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.

Key words: Unsteady convection-diffusion equation, High order compact scheme, ADI method, Stability.

Mathematics Subject Classification:

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This paper has been published in Journal of Computational Physics, Vol. 198, pp. 1-9, (2004).

Technical Report 374-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003.

The research work of the authors was supported in part by the U.S. National Science Foundation under grants CCR-9988165, CCR-0092532, ACR-0202934, and ACR-0234270, in part by the U.S. 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).