A Divergence-Free Chebyshev Collocation Procedure for Incompressible Flows with Two Non-periodic Directions

Ravi K. Madabhushi, S. Balachandar, S. P. Vanka

Research output: Contribution to journalArticle

Abstract

The enforcement of divergence-free condition in the interior and on the boundaries of an incompressible flow with two non-periodic directions is discussed for a Chebyshev collocation formulation. An influence matrix technique along with a correction methodology is used to satisfy the continuity equation everywhere in the domain. Details of implementing this procedure in a collocation method are presented. An efficient solution procedure based on matrix diagonalization has been used to solve the resulting full matrices. Two test problems: (a) flow in a driven square cavity, and (b) fully-developed laminar flow in a square duct subject to a three-dimensional perturbation are studied. Run-time statistics (CPU, memory, MFLOPS) of the solution procedure are presented for representative grid sizes.

Original languageEnglish (US)
Pages (from-to)199-206
Number of pages8
JournalJournal of Computational Physics
Volume105
Issue number2
DOIs
StatePublished - Apr 1993

ASJC Scopus subject areas

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

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