Extreme-scale Direct Numerical Simulation of Incompressible Turbulence on the Heterogeneous Many-core System

Direct numerical simulation (DNS) is a technique that directly solves the fluid Navier-Stokes equations with high spatial and temporal resolutions, which has driven much research regarding the nature of turbulence. For high-Reynolds number (Re) incompressible turbulence of particular interest, where the nondimensional Re characterizes the flow regime, the application of DNS is hindered by the fact that the numerical grid size (i.e., the memory requirement) scales with Re³, while the overall computational cost scales with Re⁴. Recent studies have shown that developing efficient parallel methods for heterogeneous many-core systems is promising to solve this computational challenge.

We develop PowerLLEL++, a high-performance and scalable implicit finite difference solver for heterogeneous many-core systems, to accelerate the extreme-scale DNS of incompressible turbulence. To achieve this goal, an adaptive multi-level parallelization strategy is first proposed to fully exploit the multi-level parallelism and computing power of heterogeneous many-core systems. Second, hierarchical-memory-adapted data reuse/tiling strategy and kernel fusion are adopted to improve the performance of memory-bound stencil-like operations. Third, a parallel tridiagonal solver based on the parallel diagonal dominant (PDD) algorithm is developed to minimize the number of global data transposes. Fourth, three effective communication optimizations are implemented by Remote Direct Memory Access (RDMA) to maximize the performance of the remaining global transposes and halo exchange.

Results show that the solver exploits the heterogeneous computing power of the new Tianhe supercomputer and achieves a speedup of up to 10.6× (against the CPU-only performance). Linear strong scaling is obtained with a grid size of up to 25.8 billion.