Challenges in Fluid Flow Simulations Using Exascale Computing

In this paper, we briefly discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we sketch the computational complexities of finite difference (FD) method, pseudo-spectral method, and fast Fourier transform (FFT). The global data communication among the compute cores brings down the efficiency of pseudo-spectral codes and FFT. A FD solver involves relatively lower data communication. However, an incompressible FD flow solver has a pressure Poisson equation, whose computation in multigrid scheme is quite expensive. Hence, a comparative study between the two sets of solvers on exascale system would be valuable. In this paper, we report a comparative performance analysis between a FD code and a spectral code on a relatively smaller grid using 1024 compute cores of Shaheen II; here, the FD code yields comparable accuracy to the spectral code, but it is relatively slower. The above features need to be retested on much larger grids with many more processors.