We have developed an effective method for accelerating fluid dynamics calculations with high-order precision on graphics processing units (GPUs). This is done by efficient use of GPU memory with cache blocking and by dividing computation algorithms into memory efficient chunks. Our Nvidia CUDA based, proof of concept code Astaroth is able to achieve 3.6 times speedup in comparison to the reference code, which in practice allows for a week-long turbulence simulation to be performed within a couple of days. The method is published in Pekkilä, Väisälä et al. (2017).