A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion problems

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27 Citations (Scopus)

Abstract

We derive a high-order compact alternating direction implicit (ADI) method for solving three-dimentional unsteady convection-diffusion problems. The method is fourth-order in space and second-order in time. It permits multiple uses of the one-dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second-order Douglas-Gunn ADI method and the spatial fourth-order compact scheme by Karaa.

Original languageEnglish
Pages (from-to)983-993
Number of pages11
JournalNumerical Methods for Partial Differential Equations
Volume22
Issue number4
DOIs
Publication statusPublished - Jul 2006

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Alternating Direction Implicit Method
Convection-diffusion Problems
Fourth Order
Higher Order
Compact Scheme
Three-dimensional
Fourier analysis
Unconditionally Stable
Fourier Analysis
Tridiagonal matrix
Numerical Experiment
Computing
Experiments
Convection
Standards

Keywords

  • ADI method
  • High-order compact scheme
  • Stability
  • Unsteady convection-diffusion problem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

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abstract = "We derive a high-order compact alternating direction implicit (ADI) method for solving three-dimentional unsteady convection-diffusion problems. The method is fourth-order in space and second-order in time. It permits multiple uses of the one-dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second-order Douglas-Gunn ADI method and the spatial fourth-order compact scheme by Karaa.",
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AB - We derive a high-order compact alternating direction implicit (ADI) method for solving three-dimentional unsteady convection-diffusion problems. The method is fourth-order in space and second-order in time. It permits multiple uses of the one-dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second-order Douglas-Gunn ADI method and the spatial fourth-order compact scheme by Karaa.

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KW - Stability

KW - Unsteady convection-diffusion problem

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