A low-communication-overhead parallel method for the 3D incompressible Navier-Stokes equations

TL;DR

This paper introduces a parallel computational method with minimal communication overhead for solving 3D incompressible Navier-Stokes equations, enabling efficient large-scale turbulence simulations.

Contribution

A novel low-communication parallel algorithm combining a fully-explicit projection method with a PDD solver for pressure, achieving high scalability and efficiency.

Findings

Excellent scalability up to 10,000 cores

Accurate turbulence statistics at high Reynolds numbers

Reduced communication overhead in parallel computations

Abstract

This paper presents a low-communication-overhead parallel method for solving the 3D incompressible Navier-Stokes equations. A fully-explicit projection method with second-order space-time accuracy is adopted. Combined with fast Fourier transforms, the parallel diagonal dominant (PDD) algorithm for the tridiagonal system is employed to solve the pressure Poisson equation, differing from its recent applications to compact scheme derivatives computation (Abide et al. 2017) and alternating-direction-implicit method (Moon et al. 2020). The number of all-to-all communications is decreased to only two, in a 2D pencil-like domain decomposition. The resulting MPI/OpenMP hybrid parallel code shows excellent strong scalability up to $10^4$ cores and small wall-clock time per timestep. Numerical simulations of turbulent channel flow at different friction Reynolds numbers ($Re_{\tau}$ = 550, 1000, 2000) have been conducted and the statistics are in good agreement with the reference data. The proposed method allows massively simulation of wall turbulence at high Reynolds numbers as well as many other incompressible flows.