Challenges in fluid flow simulations using Exascale computing

TL;DR

This paper examines the challenges of adapting hydrodynamic codes to exascale supercomputers, focusing on computational complexities and scalability issues of different numerical methods.

Contribution

It analyzes the scalability of various hydrodynamic simulation methods on exascale systems, highlighting the potential of finite difference and finite volume codes.

Findings

FFT scaling may saturate at 500,000 processors

Finite difference and finite volume codes scale well beyond a million processors

Spectral-element and Fourier continuation methods could also scale effectively

Abstract

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.