Geodesic
Numerical convergence of the random vortex method for complex flows
I. Mortazavi1 ; P. Micheau1 ; A. Giovannini2
1 Laboratoire de mécanique de Lille URA CNRS 1441 Bd. Paul Langevin 59650 Villeneuve d'Ascq, France
2 Laboratoire de modélisation en mécanique des fluides de Toulouse 118 route de Narbonne 33602 Toulouse, France
ESAIM. Proceedings, Tome 1 (1996), pp. 521-538.

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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. G(sheet or blob strength) and h (sheet length or core radius of a blob) and the third one to the discretization of time, ?t 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.
DOI : 10.1051/proc:1996021

I. Mortazavi 1 ; P. Micheau 1 ; A. Giovannini 2

1 Laboratoire de mécanique de Lille URA CNRS 1441 Bd. Paul Langevin 59650 Villeneuve d'Ascq, France
2 Laboratoire de modélisation en mécanique des fluides de Toulouse 118 route de Narbonne 33602 Toulouse, France 
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     title = {Numerical convergence of the random vortex method for complex flows},
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I. Mortazavi; P. Micheau; A. Giovannini. Numerical convergence of the random vortex method for complex flows. ESAIM. Proceedings, Tome 1 (1996), pp. 521-538. doi : 10.1051/proc:1996021. http://geodesic.mathdoc.fr/articles/10.1051/proc:1996021/

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