The Computational Fluid Dynamics code OVERFLOW includes as one of its solver options an algorithm which is a fairly small piece of code but which accounts for a significant portion of the total computational time. This paper studies some of the issues in accelerating this piece of code by using a Graphics Processing Unit (GPU). The algorithm needs to be modified to be suitable for a GPU and attention needs to be given to 64-bit and 32-bit arithmetic. Interestingly, the work done for the GPU produced ideas for accelerating the CPU code and led to significant speedup on the CPU.