Vortex methods. I. Convergence in three dimensions

Authors:
J. Thomas Beale and Andrew Majda

Journal:
Math. Comp. **39** (1982), 1-27

MSC:
Primary 65M15; Secondary 76C05

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658212-5

MathSciNet review:
658212

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658212-5

Keywords:
Vortex method, incompressible flow

Article copyright:
© Copyright 1982
American Mathematical Society