GPU-accelerated computing is becoming a popular technology due to the emergence of techniques such as OpenACC, which makes it easy to port codes in their original form to GPU systems using compiler directives, and thereby speeding up computation times relatively simply. In this study we have developed an OpenACC implementation of the high order finite difference CFD solver ESSENSE for simulating compressible flows. The solver is based on summation-by-part form difference operators, and the boundary and interface conditions are weakly implemented using simultaneous approximation terms. This case study focuses on porting code to GPUs for the most time-consuming parts namely sparse matrix vector multiplications and the evaluations of fluxes. The resulting OpenACC implementation is used to simulate the Taylor-Green vortex which produces a maximum speed-up of 61.3 on a single V100 GPU by compared to serial CPU version.