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On the Accuracy of Vortex Methods at Large Times

  • J. Thomas Beale
Part of the The IMA Volumes in Mathematics and Its Applications book series (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.

Keywords

Velocity Field Particle Velocity Point Vortex Velocity Error Inviscid Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • J. Thomas Beale
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA

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