Accuracy of straight-line segmentation applied to curvilinear vortex filaments

The numerical accuracy of straight-line segmentation of a general curviline ar vortex filament is rigorously examined using the vortex ring problem as a basis. The discretization approach is shown to be second-order accurate f or both an inviscid (potential) vortex and a viscous vortex with a finite c ore size. It is further shown that a higher order of accuracy can be obtain ed using numerical analysis techniques such as Richardson's extrapolation. The analysis also proves that with reasonably small discretization the stra ight-line segmentation approach can be successfully applied in free-vortex wake models without any special treatment for the self-induced velocity res ulting from vortex curvature.