Study of Small-Scale Statistics of Large Reynolds Number Turbulence by Extreme-Scale Computation
ORAL · Invited
Abstract
In the study of turbulence, it is often assumed that there are simple universal laws in the statistics of turbulence at sufficiently large Reynolds number (Re) and sufficiently small scales. Extreme-scale computation, in particular direct numerical simulation (DNS), can contribute much to the understanding of the statistics and to the exploration of the laws, if they exist.
Efforts have been made from this viewpoint. This talk presents a review of such efforts, with emphasis on those by a series of DNSs of forced turbulence with up to 24,576^3 grid points performed on the supercomputer K or FUGAKU at RIKEN, Japan. The 24,576^3 grid point DNS uses 65,536 nodes on FUGAKU. The DNSs use a de-aliased pseudo-spectral method with double precision arithmetic and a fourth-order Runge-Kutta method. Most of the computation time is consumed by the all-to-all communication in the Fast Fourier Transforms. Results by the DNSs include those on (i) the turbulence energy spectrum and second-order velocity structure functions, and (ii) statistics associated with fourth-order two-point moments of velocity gradients. The results on (i) suggest that, in a sense, the Taylor-scale Reynolds number of 2000 or so may still be too small to test theories of intermittency at small scales. The results on (ii) provide new insights into the anisotropic local structures of intense enstrophy (squared vorticity) regions.
In studying turbulence, one often assumes its statistics to be under certain idealized conditions, such as infinite Re, homogeneity, isotropy, and so on. On the other hand, in a strict sense, there are generally gaps between such idealized conditions and those realizable in DNS. This talk presents also a review of efforts to understand the effects of the gaps on the statistics from a viewpoint similar to that of linear response theory in the statistical mechanics of systems at or near thermal equilibrium.
The author gratefully acknowledges the collaboration of N. Okamoto, T. Ishihara, and M. Yokokawa in the preparation of this talk.
Efforts have been made from this viewpoint. This talk presents a review of such efforts, with emphasis on those by a series of DNSs of forced turbulence with up to 24,576^3 grid points performed on the supercomputer K or FUGAKU at RIKEN, Japan. The 24,576^3 grid point DNS uses 65,536 nodes on FUGAKU. The DNSs use a de-aliased pseudo-spectral method with double precision arithmetic and a fourth-order Runge-Kutta method. Most of the computation time is consumed by the all-to-all communication in the Fast Fourier Transforms. Results by the DNSs include those on (i) the turbulence energy spectrum and second-order velocity structure functions, and (ii) statistics associated with fourth-order two-point moments of velocity gradients. The results on (i) suggest that, in a sense, the Taylor-scale Reynolds number of 2000 or so may still be too small to test theories of intermittency at small scales. The results on (ii) provide new insights into the anisotropic local structures of intense enstrophy (squared vorticity) regions.
In studying turbulence, one often assumes its statistics to be under certain idealized conditions, such as infinite Re, homogeneity, isotropy, and so on. On the other hand, in a strict sense, there are generally gaps between such idealized conditions and those realizable in DNS. This talk presents also a review of efforts to understand the effects of the gaps on the statistics from a viewpoint similar to that of linear response theory in the statistical mechanics of systems at or near thermal equilibrium.
The author gratefully acknowledges the collaboration of N. Okamoto, T. Ishihara, and M. Yokokawa in the preparation of this talk.
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Presenters
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Yukio Kaneda
Nagoya University
Authors
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Yukio Kaneda
Nagoya University