A vortex filament scheme, termed the GVFS or gridfree vortex filament scheme, in which the vorticity field away from the immediate vicinity of solid boundaries was represented by convecting, gridfree vortex tubes, was used to simulate flow over a backward-facing step with curved edges. The backward-facing step geometry, which possesses a fixed separation point at the step edge, is largely used to study the physics of separation, reattachment, recirculation, and reattachment. Changes to the vortex filament scheme, termed the vortex insertion scheme, were added to the original vortex filament scheme which consisted of inserting vortex tubes into the flow immediately downstream of the step edge based on local vorticity. Running the vortex filament scheme in conjunction with the vortex insertion scheme produced a separated region suitable for comparison to flow over a backward-facing step with straight edges. By utilizing an alternative definition of structure which considered the entirety of the vorticity field it was demonstrated that roller vortices which form in the separated region: (i) result from the roll-up of fluid induced by the shear layer in the separated region, (ii) extend across the span but possess spanwise gaps which underlie the extensions of furrows which convect into the separated region, and (iii) break up due to shearing motion generated by the shear layer in the separated region. It was also discovered that flapping of the shear layer in the separated region results from changes in the spanwise positions of the furrows. The results of the present thesis demonstrate that vortex filament schemes are useful tools to tie together the structure in the upstream boundary layer of a step flow with the structure present in the mixing layer that occurs downstream of the step edge. In addition, a tentative connection was found between the structural make-up of the fluid upstream of the step edge and reattachment. This potential link was used to suggest an area for future research.