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Computational Fluid Dynamics and Reacting Gas Flows pp 19–32Cite as

On the Accuracy of Vortex Methods at Large Times

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 12))

Abstract

Vortex methods simulate incompressible flow, without viscosity or at high Reynolds number, by a collection of computational elements of vorticity which are transported along computed particle paths. The velocity field can be computed from the vorticity in order to move the elements forward in time. Here we will survey the formulation and convergence theory of such methods, primarily for inviscid flow without boundaries in two or three dimensions. We also discuss a modification of the basic method intended to improve accuracy at later times and illustrate its performance with a simple test problem. It is found that the error is significantly reduced in this case. This modified method can be shown to converge, and details of the proof will be given elsewhere. Very similar ideas have been experimented with by Chris Anderson, and it is a pleasure to thank him for his helpful comments and suggestions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27706, USA

    J. Thomas Beale

Authors
  1. J. Thomas Beale
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, 90024, USA

    Bjorn Engquist

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Andrew Majda

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

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© 1988 Springer-Verlag New York Inc.

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Beale, J.T. (1988). On the Accuracy of Vortex Methods at Large Times. In: Engquist, B., Majda, A., Luskin, M. (eds) Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3882-9_2

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  • DOI: https://doi.org/10.1007/978-1-4612-3882-9_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8388-1

  • Online ISBN: 978-1-4612-3882-9

  • eBook Packages: Springer Book Archive

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