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

Beale, J. Thomas; Majda, Andrew

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

Vortex methods. II. Higher order accuracy in two and three dimensions
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by J. Thomas Beale and Andrew Majda PDF

Math. Comp. 39 (1982), 29-52 Request permission

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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