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Zbl 1053.65067
Karaa, Samir; Zhang, Jun
High order ADI method for solving unsteady convection-diffusion problems. (English)
[J] J. Comput. Phys. 198, No. 1, 1-9 (2004). ISSN 0021-9991

Summary: 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 {\it B. J. Noye} and {\it H. H. Tan} [Int. J. Numer. Methods Eng. 26, No.~7, 1615--1629 (1988; Zbl 0638.76104)].

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35K15 Second order parabolic equations, initial value problems
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: Unsteady convection-diffusion equation; High order compact scheme; ADI method; Stability; comparison of methods; alternating direction implicit method; algorithm; Numerical experiments; Peaceman-Rachford method

Citations: Zbl 0638.76104

Cited in: Zbl 1219.65092 Zbl 1104.65086 Zbl 1089.65092

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