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Mathematics of Computation

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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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Keywords: Vortex method, incompressible flow
Article copyright: © Copyright 1982 American Mathematical Society