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

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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
Issue number4
Publication statusPublished - Jul 2006



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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

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