Abstract
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.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
van Beckum, F.P.H. (1976). Two coordinate systems description of viscous flow past a circular cylinder. In: van de Vooren, A.I., Zandbergen, P.J. (eds) Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. Lecture Notes in Physics, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08004-X_303
Download citation
DOI: https://doi.org/10.1007/3-540-08004-X_303
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08004-6
Online ISBN: 978-3-540-37548-7
eBook Packages: Springer Book Archive