Convergence of the random vortex method in two dimensions

Long, Ding-Gwo

doi:10.1090/S0894-0347-1988-0958446-1

Convergence of the random vortex method in two dimensions
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by Ding-Gwo Long

J. Amer. Math. Soc. 1 (1988), 779-804

DOI: https://doi.org/10.1090/S0894-0347-1988-0958446-1

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Abstract:

A theoretical framework for analyzing the random vortex method is presented. It extends and modifies the analysis of the inviscid vortex method in a natural and unified manner. The rate of convergence of the random vortex method in two dimensions is obtained by analyzing the consistency error and justifying the stability estimate. The sampling error introduced by the random motions of finitely many vortices is the dominant component of the consistency error in terms of order. It is estimated by applying Bennett’s inequality.

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