High order ADI method for solving unsteady convection-diffusion problems

Authors:
Samir Karaa;Jun Zhang
Affiliations:
Department of Mathematics and Statistics, Sultan Qaboos University, Sultanate of Oman and Laboratory for High-Performance Scientific Computing and Computer Simulation, Department of Computer Scien ...;Laboratory for High-Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY
Venue:
Journal of Computational Physics
Year:
2004

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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.