Accuracy of vortex methods

The accuracy of the vortex method depends on the choice of the cutoff function, of the cutoff length delta and on the initialization of the vorticity distribution. The practical effect of the choices on the vortex method for inviscid flows in the absence of boundaries was investigated. It is shown that the vorticity is radially symmetric and has bounded support. The consistency error and its components, the smoothing error and the discretization error for high order cutoff functions and several values of the cutoff length delta are considered. It is indicated that for smooth flows, high order cutoffs improve the accuracy of the approximation. The best value of delta is larger than h, the initial distance between the vortices; it is time dependent in the sense that longer time integration requires a larger delta. The optimal choice of delta is insensitive to the smoothness of the flow. If delta is close to h then the accuracy is lost in a relatively short time. This loss of accuracy is caused by the growth of the discretization error.