Vortex methods. II. Higher order accuracy in two and three dimensions

Authors:
J. Thomas Beale and Andrew Majda

Journal:
Math. Comp. **39** (1982), 29-52

MSC:
Primary 65M15; Secondary 76C05

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658213-7

MathSciNet review:
658213

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658213-7

Keywords:
Vortex method,
incompressible flow

Article copyright:
© Copyright 1982
American Mathematical Society