Abstract

This paper presents a low-communication-overhead parallel method for direct numerical simulations of the 3D incompressible wall turbulence. 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. 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 and the recent scaling theories [Chen, X. and K. R. Sreenivasan. 2021. “Reynolds Number Scaling of the Peak Turbulence Intensity in Wall Flows.” Journal of Fluid Mechanics 908: R3. doi:10.1017/jfm.2020.991].