Free space optical links between the ground and space may be severely degraded by atmospheric turbulence. Adaptive Optics, a technique allowing partial correction of this degradation, is beginning to see use in the field with the potential to achieve more robust and higher bandwidth links. Here we present a simulation tool, FAST, which utilises an analytical Fourier domain Adaptive Optics model developed for astronomy. Using the reciprocity principle, the simulation may be applied either to downlink post-compensated or uplink pre-compensated beams. We show that FAST gives similar results to full end-to-end simulations with wave-optical propagation whilst being between 10 and 200 times faster, enabling the characterisation of optical links with complex Adaptive Optics systems in timely fashion.