An exponential high-order compact ADI method for 3D unsteady convection-diffusion problems

Yongbin Ge, Zhen F. Tian, Jun Zhang

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


In this article, we develop an exponential high order compact alternating direction implicit (EHOC ADI) method for solving three dimensional (3D) unsteady convection-diffusion equations. The method, which requires only a regular seven-point 3D stencil similar to that in the standard second-order methods, is second order accurate in time and fourth-order accurate in space and unconditionally stable. The resulting EHOC ADI scheme in each alternating direction implicit (ADI) solution step corresponding to a strictly diagonally dominant matrix equation can be solved by the application of the one-dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. Numerical experiments for three test problems are carried out to demonstrate the performance of the present method and to compare it with the classical Douglas-Gunn ADI method and the Karaa's high-order compact ADI method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

Original languageEnglish
Pages (from-to)186-205
Number of pages20
JournalNumerical Methods for Partial Differential Equations
Issue number1
StatePublished - Jan 2013


  • ADI method
  • exponential
  • high-order compact scheme
  • stability
  • three-dimensional unsteady convection-diffusion equation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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