A high-order ADI method for parabolic problems with variable coefficients

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Abstract

A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.

Original languageEnglish
Pages (from-to)109-120
Number of pages12
JournalInternational Journal of Computer Mathematics
Volume86
Issue number1
DOIs
Publication statusPublished - Jan 2009

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Keywords

  • 2D incompressible Navier-Stokes equations
  • ADI method
  • Driven cavity flow
  • High-order compact scheme

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Computational Theory and Mathematics

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