High order ADI method for solving unsteady convection-diffusion problems

Samir Karaa; Jun Zhang

doi:10.1016/j.jcp.2004.01.002

High order ADI method for solving unsteady convection-diffusion problems

Samir Karaa, Jun Zhang^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

178 Citations (Scopus)

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	https://doi.org/10.1016/j.jcp.2004.01.002
Publication status	Published - Jul 20 2004

Keywords

ADI method
High order compact scheme
Stability
Unsteady convection-diffusion equation

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2004.01.002

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title = "High order ADI method for solving unsteady convection-diffusion problems",

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.",

keywords = "ADI method, High order compact scheme, Stability, Unsteady convection-diffusion equation",

author = "Samir Karaa and Jun Zhang",

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).",

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doi = "10.1016/j.jcp.2004.01.002",

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T1 - High order ADI method for solving unsteady convection-diffusion problems

AU - Karaa, Samir

AU - Zhang, Jun

N1 - 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).

PY - 2004/7/20

Y1 - 2004/7/20

N2 - 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.

AB - 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.

KW - ADI method

KW - High order compact scheme

KW - Stability

KW - Unsteady convection-diffusion equation

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

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High order ADI method for solving unsteady convection-diffusion problems

Abstract

Keywords

ASJC Scopus subject areas

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