Numerical Convergence of the Random Vortex Method for Complex Flows

Vortex methods rely principally on a discretization of the continuous two-dimensional time dependent vorticity eld into a large number of vortex \blobs", whose position and strength determine the underlying velocity eld. In this paper, the convergence of the random vortex method (RVM) for a complex ow 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. t. Two principal events are observed. First, the computation works but the convergence is not attained. Second, the computation fails. The rst behaviour is attributed to a lack of accuracy while the second is attributed to a lack of numerical stability. Once the stability conditions are satissed, decreasing the value of the parameters always leads to convergence.