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

Computer Science

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

188 Scopus citations

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
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).

Funding

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).

Funders	Funder number
Japan Research Organization for Information Science and Technology
RIST
National Science Foundation Arctic Social Science Program	CCR-0092532, ACR-0234270, ACR-0202934, CCR-9988165
National Science Foundation Arctic Social Science Program
U.S. Department of Energy Oak Ridge National Laboratory U.S. Department of Energy National Science Foundation National Energy Research Scientific Computing Center	DE-FG02-02ER45961
U.S. Department of Energy Oak Ridge National Laboratory U.S. Department of Energy National Science Foundation National Energy Research Scientific Computing Center
Kentucky Science and Engineering Foundation	KSEF-02-264-RED-002
Kentucky Science and Engineering Foundation

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

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10.1016/j.jcp.2004.01.002

Cite this

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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",

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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.

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KW - Stability

KW - Unsteady convection-diffusion equation

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High order ADI method for solving unsteady convection-diffusion problems

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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