Challenges in fluid flow simulations using Exascale computing

In this paper, I discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we describe the computational complexities of finite difference method, pseudo-spectral method, and Fast Fourier Transform (FFT). We show how global data communication among the processors brings down the efficiency of pseudo-spectral codes and FFT. It is argued that FFT scaling may saturate at 1/2 million processors. However, finite difference and finite volume codes scale well beyond million processors, hence they are likely candidates to be tried on exascale systems. The codes based on spectral-element and Fourier continuation, that are more accurate than finite difference, could also scale well on such systems.