Effects of arithmetic precision in large-scale direct numerical simulation of incompressible turbulence in a periodic box

The recent development of parallel computers enables us to perform large-scale direct numerical simulations (DNS) of turbulence and to analyze physical quantities with a wider range of scale ratios. One issue to be cared about in such simulations is the effects of arithmetic precision. In this study, to investigate the effects on large-scale DNS, we performed DNSs of incompressible turbulence in a periodic box with single- and double-precision at R_λ=170 and R_λ=268 based on a spectral method at spatial resolution k_maxη∼4 and compared the results, where R_λ is the Reynolds number based on the Taylor microscale, k_max is the maximum retained wavenumber, and η is the Kolmogorov length scale. Particular attention is paid to the time evolution of the spatial maximum of local enstrophy and that of the local energy-dissipation rate. The DNSs show that for R_λ=268, unlike the case for R_λ=170, the difference between the time evolution by double-precision and that of single-precision is not significant for a short-time range (t < 1.3T) but becomes significant for a long-time range (t > 1.3T). Here, T is a large-scale characteristic timescale. The presentation will also report results regarding some other quantities (including the temporally averaged PDFs).