Superconducting nanowire detectors fed by single mode fibres are essential to minimize dark counts in a quantum communication receiver. Efficient coupling of the received light to the single mode fibre is fundamental for the system performance, but it gets deeply affected by the atmospheric turbulence. Adaptive Optics measure and correct for the atmosphere effect on the light optimising the fibre coupling. An Adaptive Optics system is proposed to be installed at the ground station that will receive quantum key distribution from a geostationary satellite. Numerical simulations have been performed for this scenario; the improvement in the fibre coupling have been assessed with and without atmospheric turbulence correction. The present paper encapsulates the simulation framework and main findings, showing the potential for this technology in the quantum communications niche.