Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings, Vol. 1, 1996, pp. 521-538

Numerical Convergence of the Random Vortex Method for Complex Flows

I. Mortazavi, P. Micheau

A. Giovannini

Abstract

Vortex methods rely principally on a discretization of the continuous two-dimensional time dependent vorticity field into a large number of vortex "blobs", whose position and strength determine the underlying velocity field. In this paper, the convergence of the random vortex method (RVM) for a complex flow is studied in function of three discretization parameters. Two of these parameters are related to the spatial discretization of the vorticity, i.e. (sheet or blob strength) and h (sheet length or core radius of a blob) and the third one to the discretization of time, i.e. . Two principal events are observed. First, the computation works but the convergence is not attained. Second, the computation fails. The first behaviour is attributed to a lack of accuracy while the second is attributed to a lack of numerical stability. Once the stability conditions are satisfied, decreasing the value of the parameters always leads to convergence.

Vortex Flows and Related Numerical Methods II
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