Three-dimensional viscous flow through a rotating channel: A pseudospectral matrix method approach

H. B. Chen*, K. Nandakumar, W. H. Finlay, H. C. Ku

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

A Fourier-Chebyshev pseudospectral method is used for the numerical simulation of incompressible flows in a three-dimensional channel of square cross-section with rotation. Realistic, non-periodic boundary conditions that impose no-slip conditions in two directions (spanwise and vertical directions) are used. The Navier-Stokes equations are integrated in time using a fractional step method. The Poisson equations for pressure and the Helmholtz equation for velocity are solved using a matrix diagonalization (eigenfunction decomposition) method, through which we are able to reduce a three-dimensional matrix problem to a simple algebraic vector equation. This results in signficant savings in computer storage requirement, particularly for large-scale computations. Verification of the numerical algorithm and code is carried out by comparing with a limiting case of an exact steady state solution for a one-dimensional channel flow and also with a two-dimensional rotating channel case. Two-cell and four-cell two-dimensional flow patterns are observed in the numerical experiment. It is found that the four-cell flow pattern is stable to symmetrical disturbances but unstable to asymmetrical disturbances.

Original languageEnglish
Pages (from-to)379-396
Number of pages18
JournalInternational Journal for Numerical Methods in Fluids
Volume23
Issue number4
DOIs
StatePublished - 30 Aug 1996
Externally publishedYes

Keywords

  • Eigenvalue decomposition
  • Pseudospectral matrix method
  • Rotating flow
  • Three-dimensional rectangular channel
  • Two- and four-cell flow pattern

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