Accuracy of straight-line segmentation applied to curvilinear vortex filaments

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