High order ADI method for solving unsteady convection-diffusion problems

Samir Karaa, Jun Zhang

Research output: Contribution to journalArticle

135 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 languageEnglish
Pages (from-to)1-9
Number of pages9
JournalJournal of Computational Physics
Volume198
Issue number1
DOIs
Publication statusPublished - Jul 20 2004

Fingerprint

alternating direction implicit methods
Fourier analysis
convection
Experiments
Convection

Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

High order ADI method for solving unsteady convection-diffusion problems. / Karaa, Samir; Zhang, Jun.

In: Journal of Computational Physics, Vol. 198, No. 1, 20.07.2004, p. 1-9.

Research output: Contribution to journalArticle

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