Vortex methods. ii: Higher order accuracy in two and three dimensions

J. Thomas Beale, Andrew Majda

Research output: Contribution to journalArticle

Abstract

In an earlier paper the authors introduced a new version of the vortex method for three-dimensional, incompressible flows and proved that it converges to arbitrarily high order accuracy, provided we assume the consistency of a discrete approximation to the Biot-Savart Law. We prove this consistency statement here, and also derive substantially sharper results for two-dimensional flows. A complete, simplified proof of convergence in two dimensions is included.

Original languageEnglish (US)
Pages (from-to)29-52
Number of pages24
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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