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

J. Thomas Beale; Andrew Majda

doi:10.1090/S0025-5718-1982-0658213-7

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

J. Thomas Beale, Andrew Majda

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	29-52
Number of pages	24
Journal	Mathematics of Computation
Volume	39
Issue number	159
DOIs	https://doi.org/10.1090/S0025-5718-1982-0658213-7
State	Published - Jul 1982

Keywords

Incompressible flow
Vortex method

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-1982-0658213-7

Cite this

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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.",

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AB - 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.

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KW - Vortex method

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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