Two coordinate systems description of viscous flow past a circular cylinder

F.P.H. van Beckum

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    Two dimensional steady viscous exterior flow is often treated as an elliptic problem within a finite region, bounded by a big circle. Solutions by means of Fourier expansions or discretisation on a polar grid will only give reliable results for low Reynolds numbers. In the present paper an example of a transformation is given, that maps the entire vorticity field onto a rectangle so that: (a) the vorticity equation can develop its parabolic character, (b) the wake in the far field comes out properly, and (c) the restriction to low Reynolds numbers is removed. For the elliptic stream-function equation the polar system is retained.

    This two coordinate systems description has been studied for a linearized version of the Navier-Stokes equations obtained by assuming a fixed velocity field v(o) in the convection term. The first results ζ and ψ are qualitatively so similar to the final solutions known from literature, that an iteration process, suggested-by deriving a new velocity field v(1) from ϕ, can be expected to show rapid convergence.
    Original languageEnglish
    Title of host publicationProceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede
    EditorsAdriaan I. van de Vooren, Pieter J. Zandbergen
    Place of PublicationBerlin, Heidelberg
    ISBN (Electronic)978-3-540-37548-7
    ISBN (Print)978-3-540-08004-6
    Publication statusPublished - 1976
    Event5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976 - Twente University, Enschede, Netherlands
    Duration: 28 Jun 19762 Jul 1976
    Conference number: 5

    Publication series

    NameLecture Notes in Physics
    ISSN (Print)0075-8450
    ISSN (Electronic)1616-6361


    Conference5th International Conference on Numerical Methods in Fluid Dynamics, NMFD 1976
    Abbreviated titleNMFD


    • Convection term
    • Polar system
    • Vorticity equation
    • Vorticity distribution
    • Polar grid

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