Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence

Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases have not been explored in detail and limits the optimal utilization of new high-performance computing systems. In this work, the effect of reduced precision is studied using four diverse computational fluid dynamics (CFD) solvers (two incompressible, Neko and Simson, and two compressible, PadeLibs and SSDC) using four test cases: turbulent channel flow at Retau = 550 and higher, forced transition in a channel, flow over a cylinder at ReD = 3900, and compressible flow over a wing section at Rec = 50000. We observe that the flow physics are remarkably robust with respect to reduction in lower floating-point precision, and that often other forms of uncertainty, due to for example time averaging, often have a much larger impact on the computed result. Our results indicate that different terms in the Navier-Stokes equations can be computed to a lower floating-point accuracy without affecting the results. In particular, standard IEEE single precision can be used effectively for the entirety of the simulation, showing no significant discrepancies from double-precision results across the solvers and cases considered. Potential pitfalls are also discussed.

💡 Research Summary

This paper presents a comprehensive, multi-solver investigation into the effects of reduced floating-point precision on high-fidelity scale-resolving simulations of turbulence, such as Direct Numerical Simulation (DNS) and wall-resolved Large Eddy Simulation (LES). Motivated by the performance and energy efficiency benefits of lower-precision arithmetic on modern hardware, the study addresses the CFD community’s skepticism regarding potential accuracy trade-offs.

The methodology is robust and diverse. It examines floating-point formats from FP64 down to 8-bit types. The core of the study employs four distinct CFD solvers representing different numerical approaches: the incompressible solvers Neko (Spectral Element Method) and Simson (Pseudospectral), and the compressible solvers PadeLibs (high-order Compact Finite Difference) and SSDC (Discontinuous Galerkin Spectral Element Method). These solvers are applied to four canonical test cases: turbulent channel flow at Reτ up to 2000, forced transition in a channel (Tollmien-Schlichting waves), flow over a circular cylinder at ReD=3900, and compressible flow over a NACA-0012 airfoil section at Rec=50,000. This selection covers internal flows, transition, external separated flows, and compressibility effects.

The central finding is that the statistics of turbulent flows are remarkably robust to reductions in floating-point precision. Across all solvers and cases, simulations conducted entirely in standard IEEE single precision (FP32) showed no statistically significant discrepancies in mean flow quantities and Reynolds stresses compared to their double-precision (FP64) counterparts. The research indicates that individual terms within the Navier-Stokes equations can be computed with lower accuracy without adversely affecting the final statistical results. In some instances, uncertainties arising from other sources, such as finite time-averaging periods, had a larger impact on the results than the precision reduction itself.

The paper also discusses potential pitfalls and practical considerations. It notes that issues may arise in regimes where the viscous term becomes extremely small (very low effective Reynolds number), in regions with extreme scale disparities between variables (e.g., near walls), or in dynamical systems sensitive to minute perturbations. The authors share experiences from developing native FP32 versions of several solvers, offering guidance for code adaptation.

In conclusion, this work provides strong empirical evidence that single-precision arithmetic can be reliably and effectively used for the entirety of high-fidelity scale-resolving turbulence simulations across a wide range of flow types and numerical methods. This finding has significant implications for leveraging the performance and energy-efficiency advantages of next-generation computing hardware in computational fluid dynamics.