Vortex methods. I: Convergence in three dimensions

J. Thomas Beale, Andrew Majda

Research output: Contribution to journalArticlepeer-review

Abstract

Recently several different approaches have been developed for the simulation of three-dimensional incompressible fluid flows using vortex methods. Some versions use detailed tracking of vortex filament structures and often local curvatures of these filaments, while other methods require only crude information, such as the vortex blobs of the two-dimensional case. Can such "crude" algorithms accurately account for vortex stretching and converge? We answer this question affirmatively by constructing a new class of "crude" three-dimensional vortex methods and then proving that these methods are stable and convergent, and can even have arbitrarily high order accuracy without being more expensive than other "crude" versions of the vortex algorithm.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalMathematics of Computation
Volume39
Issue number159
DOIs
StatePublished - Jul 1982

Keywords

  • Incompressible flow
  • Vortex method

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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