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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 658213
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0658213-7
PII: S 0025-5718(1982)0658213-7
Keywords: Vortex method, incompressible flow
Article copyright: © Copyright 1982 American Mathematical Society