Interactive visualizations of the large-scale data generated by
the DNS of isotropic turbulence on 40963 grid points
Takashi Ishihara 1,2 and Kensaku Mori 3
1Graduate School of Engineering, Nagoya University, Japan
2JST-CREST, Japan
3
Graduate School of Information Science, Nagoya University, Japan
1Introduction

Recent development of supercomputers enables us toperform large-scale numerical simulations with huge degree offreedom. High Reynolds number (Re) turbulence is one of themost challenging problems in computational fluid dynamics.
Recently it has become possible to perform direct numericalsimulations (DNS’s) of turbulence at the Taylor micro-scale
Reynolds number Rλ of O(1000) with the number of grid points
over 40963. The statistical properties of high Re turbulence canbe studied by the analysis of such DNS data (e.g. see [1-4]).
A visualization of intense vorticity iso-surfaces in DNS ofhomogeneous isotropic turbulence with 40963 grid points andRλ=1131 (figure 1 form [1]) shows that intense vorticity regions
form tube-like structures with radius of the order of theKolmogorov length scale η, and at high Re clusters of thesetubes form large-scale vortical structures of the order of theintegral length scale L. However, it is generally difficult to fully
understand the structure of high-Re turbulence in which a wide
range of scales coexists.
In order to understand the structure of high-Reynolds
number turbulence, interactive visualizations of turbulence
would be very effective. But we have to overcome thedifficulties associated with the fact that the data is so huge.
Fortunately, the recent developments of computer technology
prevail not only in supercomputers but also in workstations. So
it is expected that by using leading-edge information
technologies on a recent high-spec workstation with large
memories we can interactively visualize the large-scale data ofhigh Re turbulence.
In this paper we briefly introduce the DNS data of high-Re
turbulence on 40963 grid points, demonstrate our recent
interactive visualization, and show the results of the interactive
visualization of high-Re turbulence.
2DNS data of high Re turbulence

A series of DNS data of high Re forced turbulence wasgenerated on the Earth simulator by numerically solving theincompressible Navier-Stokes equations using an alias-freeFourier spectral method. The details of the DNS method aredescribed in [2, 4]. The maximum Taylor micro-scale Reynolds
number (Rλ=1131) was attained by the DNS with N3=40963 grid
points and kmaxη=1.0, where kmax is the maximum wavenumber.
The key parameter values in the DNS are listed in Table 1.
Table 1. Parameter values in the DNS of high Re turbulence

NReRλkmaxη

Llh4096

36500

1131

1.0

1.1

3.4 10-2

5.1 10-4Fig. 1 A visualization of high vorticity regions obtained by the DNS
of turbulence with 40963 grid points and Rλ=1131 (from [1]). High
contrast between intense vorticity regions and weak vorticity regions canbe observed.

33.1

Interactive visualization of large-scale data
Key technologies

In order to visualize the large-scale volume data generated
by the large-scale DNS of homogeneous isotropic turbulence,
we use NewVES (New virtual endoscopy software using fast
volume rendering), which was originally developed for medical
applications such as computer-aided diagnosis and wasimproved for the large-scale data. [5] NewVES uses various
optimization techniques to achieve an interactive speed; thetechniques include (1) empty volume skipping, (2) early raytermination, (3) volume segmentation and (4) multiple andadaptive resolution representation.
Since NewVES realizes fast volume rendering as softwareand uses Remote Desktop Protocol (RDP), it does not require
any special graphics card. However it requires large memory forthe visualization of large-scale volume data. NewVES uses
Streaming SIMD Extensions (SSE) and is optimized for theCPUs with multiple cores, so that its volume-rendering speed
depends on not only the performance of each CPU but also thenumber of CPUs. Table 2 shows the computer configuration that
we used for the visualizations in this paper.

Table 2. Computer configuration

ComputerProcessor
MemoryDell PowerEdge R910
Intel Xeon E7520(4 cores, 8 threads, 1.866GHz)
512GB(8GB*64)

which were recently observed and were analyzed in detail. [6,7]
It is expected that the immersive visualizations provide new
insights for our understanding of the global structure of the thinshear layers.

43.2

Interactive visualizations

To use the NewVES, we need to generate volume data forvisualization from the original scalar data, e.g. amplitude ofvorticity. In this process, the original value of the scalar (usuallyexpressed as a single-precision (4Byte) or double-precision(8Byte) floating-point number) on each point is converted into a2Byte integer in the range of [0,7000]. Therefore, a set ofvolume data for NewVES with N3 grid points is 2N3 Bytes, sothat to visualize the volume data on 40963 grid points byNewVES, 128GByte is a requisite minimum and 256GByte isrecommended for the stable performance.
Once the whole volume data are loaded on the memory ofworkstation, viewpoints, threshold values, and the otherparameters can be changed interactively in NewVES. Although
the result depends on several parameters, the performance ofabout 14 frames/sec was obtained in the volume rendering of the40963 data on the computer given in table 2. Examples of suchvisualization are shown in Figure 2.

Conclusion

New fast volume-rendering software was tested on aworkstation with 512GByte memory, using the large-scale data
generated by the DNS of isotropic turbulence on 40963 gridpoints. Interactive and immersive visualizations of such a hugedata were realized in the performance of about 14 frames/sec.
Using the software to visualize high vorticity regions, weobserved several dense regions of the intense tube-like vortices,which appear to correspond to strong thin shear layers (see e.g.
[6,7]). The global structure of the dense regions of the intense
tube-like vortices will be discussed in the conference.
Acknowledgements
The computations were carried out on the Earth Simulator at
Japan Agency for Marine-Earth Science and Technology and on
the Fx1 system at the Information Technology Center of Nagoya
University. This work was partly supported by Grant-in-Aids for
Scientific Research (C)10262495 from the Japan Society for thePromotion of Science.
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Fig 2 Examples of interactive visualization of the intense vorticity
regions obtained by the DNS of isotropic turbulence with 40963 grid
points. (a) A view from outside and (b) an immersive view.

3.3

Observations by interactive visualizations of high ReturbulenceInteractive and immersive visualizations of high Returbulence show that there are several dense regions of theintense tube-like vortices and that there is a very sharp contrast
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