Vortex methods. I

Convergence in three dimensions

J. Thomas Beale, Andrew Majda

Research output: Contribution to journalArticle

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 - 1982

Fingerprint

Vortex Method
Three-dimension
Vortex
Vortex flow
Vortex Filament
High Order Accuracy
Three-dimensional
Filament
Incompressible Flow
Incompressible Fluid
Fluid Flow
Curvature
Converge
Stretching
Flow of fluids
Simulation

Keywords

  • Incompressible flow
  • Vortex method

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Vortex methods. I : Convergence in three dimensions. / Beale, J. Thomas; Majda, Andrew.

In: Mathematics of Computation, Vol. 39, No. 159, 1982, p. 1-27.

Research output: Contribution to journalArticle

Beale, J. Thomas ; Majda, Andrew. / Vortex methods. I : Convergence in three dimensions. In: Mathematics of Computation. 1982 ; Vol. 39, No. 159. pp. 1-27.
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