60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007;
Salt Lake City, Utah
Session BS: Mini-Symposium I: Turbulence Simulations and Advanced Cyberinfrastructure
10:34 AM–12:44 PM,
Sunday, November 18, 2007
Salt Palace Convention Center
Room: Ballroom EG
Chair: P.K. Yeung, Georgia Institute of Technology
Abstract ID: BAPS.2007.DFD.BS.1
Abstract: BS.00001 : DNS of incompressible turbulence in a periodic box with up to 4096$^{3}$ grid points
10:34 AM–11:00 AM
Preview Abstract
Abstract
Author:
Yukio Kaneda
(Nagoya University)
Turbulence of incompressible fluid obeying the Navier-Stokes (NS)
equations
under periodic boundary conditions is one of the simplest
dynamical systems
keeping the essence of turbulence dynamics, and suitable for the
study of
high Reynolds number (\textit{Re}) turbulence by direct numerical
simulation (DNS).
This talk presents a review on DNS of such a system with the
number $N^{3
}$of the grid points up to 4096$^{3}$, performed on the Earth
Simulator
(ES). The ES consists of 640 processor nodes (=5120 arithmetic
processors)
with 10TB of main memory and the peak performance of 40 Tflops.
The DNSs are
based on a spectral method free from alias error. The convolution
sums in
the wave vector space were evaluated by radix-4 Fast Fourier
Transforms with
double precision arithmetic. Sustained performance of 16.4 Tflops
was
achieved on the 2048$^{3}$ DNS by using 512 processor nodes of
the ES. The
DNSs consist of two series; one is with $k_{max }$\textit{$\eta
$}$\cong $1 (Series 1) and
the other with$ k_{max }$\textit{$\eta $}$\cong $2 (Series 2),
where $k_{max}$ is the highest
wavenumber in each simulation, and \textit{$\eta $} is the
Kolmogorov length scale. In the
4096$^{3}$ DNS, the Taylor-scale Reynolds number $R_{\lambda
}\cong $1130
(675) and the ratio $L$/\textit{$\eta $} of the integral length
scale$ L$ to \textit{$\eta $ } is approximately
2133(1040), in Series 1 (Series 2). Such DNS data are expected to
shed some
light on the basic questions in turbulence research, including
those on (i)
the normalized mean rate of energy dissipation in the high
\textit{Re} limit, (ii) the
universality of energy spectrum at small scale, (iii) scale- and
\textit{Re}-
dependences of the statistics, and (iv) intermittency. We have
constructed a
database consisting of (a) animations and figures of turbulent
fields (b)
statistics including those associated with (i)-(iv) noted above, (c)
snapshot data of the velocity fields. The data size of (c) can be
very large
for large $N$. For example, one snapshot of single precision data
of the
velocity vector field of the 4096$^{3}$ DNS requires
approximately 0.8 TB.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.DFD.BS.1