Numerical Simulation is an essential part of the design and optimisation of astronomical adaptive optics systems. Simulations of adaptive optics are computationally expensive and the problem scales rapidly with telescope aperture size, as the required spatial order of the correcting system increases. Practical realistic simulations of AO systems for extremely large telescopes are beyond the capabilities of all but the largest of modern parallel supercomputers. Here we describe a more cost effective approach through the use of hardware acceleration using field programmable gate arrays. By transferring key parts of the simulation into programmable logic, large increases in computational bandwidth can be expected. We show that the calculation of wavefront sensor image centroids can be accelerated by a factor of four by transferring the algorithm into hardware. Implementing more demanding parts of the adaptive optics simulation in hardware will lead to much greater performance improvements, of up to 1000 times.