High order ADI method for solving unsteady convection-diffusion problems

Samir Karaa, Jun Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

184 Citations (Scopus)


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
Issue number1
Publication statusPublished - Jul 20 2004


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

ASJC Scopus subject areas

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


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