Numerical convergence of the random vortex method for complex flows

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.