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Issue ESAIM: Proc.
Volume 1, 1996
Vortex flows an related numerical methods II
Page(s) 521 - 538
DOI http://dx.doi.org/10.1051/proc:1996021

ESAIM: Proc., 1996, Vol. 1, pp. 521-538
DOI: 10.1051/proc:1996021

Numerical convergence of the random vortex method for complex flows

I. Mortazavi1, P. Micheau1 and 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


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. 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.



© EDP Sciences, ESAIM 1996


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