Faculty Profiles - ISHIHARA Takashi

MISC - ISHIHARA Takashi

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Ultra direct numerical simulation of turbulence on the earth simulator Reviewed

T Ishihara

COMPUTATIONAL MECHANICS, PROCEEDINGS 369 - 374 2004

Language：English Publishing type：Research paper, summary (national, other academic conference) Publisher：TSINGHUA UNIV PRESS

We recently carried out a series of DNSs of incompressible turbulence with number of grid points up to 4096(3) on the Earth Simulator (ES). The 4096(3) (ultra) DNS is 64 times the size of the largest DNS before the appearance of the ES. The DNSs consist of two groups; one is with K-max eta = 2 R-lambda = 1 and the Taylor micro scale Reynolds number R-lambda = 167 similar to 1131, while the other is with K-max eta = 2 and R-lambda = 94 similar to 675, where K-max is the maximum wave number and eta the Kolmogorov length scale. A review is given on the one-point and two-point statistics of the velocity derivatives, including the fourth-order rotational invariants I-alpha (alpha = 1...4) proposed by Siggia (1981) and the spectra of energy dissipation epsilon, enstrophy omega(2), and pressure p, obtained by the series of the DNSs on the ES. The series of the DNSs suggest that the spectra of epsilon, omega(2), and p exhibited a wave number range in which the spectra scaled with the wave number k as k(-a). Exponent a for p was in good agreement with the value obtained by assuming the joint probability distribution of the velocity field to be Gaussian, while a values for epsilon and omega(2) were very different from the Gaussian approximation values.

High-resolution direct numerical simulation of turbulence - Spectra of fourth-order velocity momenrs Reviewed

Y Kaneda, T Ishihara, M Yokokawa, K Itakura, A Uno

IUTAM SYMPOSIUM ON REYNOLDS NUMBER SCALING IN TURBULENT FLOW 74 155 - 162 2004

Language：English Publishing type：Research paper, summary (national, other academic conference) Publisher：SPRINGER

High-resolution direct numerical simulations (DNSs) of incompressible turbulence based on an alias-free spectral method were performed on the Earth Simulator. Statistics of turbulence are studied by a DNS on 1024(3) grid points with a special emphasis on the spectra of moments fourth order in velocity. A brief review is given on some results of the preliminary analysis of the data of DNSs with up to 2048(3) grid points.

E231 Velocity derivative statistics in direct numerical simulations of turbulence in a periodic box

ISHIHARA Takashi, KANEDA Yukio

2004 392 - 393 2004

Language：Japanese

The data of high resolution direct numerical simulations (DNSs) of incompressible turbulence obeying the Navier-Stokes equations in a periodic box with the number of grid points up to 4096^3 were analyzed to study the one-point statistics of the velocity-derivatives, including probability distribution functions and the fourth-order rotational invariants I_α(α=1,2,3,4) proposed by Siggia (1981). The data suggest that the values of all four I_α(α=1,2,3,4) increase with the Reynolds number R_λ and the ratios I_α/I_l tend to constants with the increase of R_λ, and that they scale with R_λ similarly to each other for large R_λ.

Similarity scaling of pressure fluctuation in turbulence Reviewed

Y Tsuji, T Ishihara

PHYSICAL REVIEW E 68 ( 2 ) 2630968-1-5 2003.8

Language：English Publisher：AMER PHYSICAL SOC

Pressure fluctuation was measured in a turbulent jet using a condenser microphone and piezoresistive transducer. The power-law exponent and proportional constant of normalized pressure spectrum are discussed from the standpoint of Kolmogorov universal scaling. The clear power law with scaling exponent close to -7/3 was confirmed in the range of 600less than or equal toR(lambda). These Reynolds numbers are much larger than those in velocity fluctuation to achieve Kolmogorov scaling. The spectral constant is not universal but depends on Reynolds numbers. Measured pressure probability density functions are compared with direct numerical simulation.

DOI： 10.1103/PhysRevE.68.026309

Anisotropic spectrum of homogeneous turbulent shear flow in a Lagrangian renormalized approximation Reviewed

K Yoshida, T Ishihara, Y Kaneda

PHYSICS OF FLUIDS 15 ( 8 ) 2385 - 2397 2003.8

Language：English Publisher：AMER INST PHYSICS

An analytical study of the anisotropic velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow is performed using a Lagrangian renormalized spectral closure approximation. The analysis shows that the spectrum in the asymptotic limit of infinitely large Reynolds numbers Re is determined by two nondimensional universal constants; theoretical estimates for the constants are provided. The anisotropic component of the spectrum at finite Re is more sensitive to large-scale turbulence structures than the isotropic component. A preliminary analysis of the effect of finite Re or the width of the inertial subrange is in qualitative agreement with direct numerical simulations. (C) 2003 American Institute of Physics.

DOI： 10.1063/1.1588307

Spectra of energy dissipation, enstrophy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box Reviewed

T Ishihara, Y Kaneda, M Yokokawa, K Itakura, A Uno

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 72 ( 5 ) 983 - 986 2003.5

Language：English Publisher：PHYSICAL SOC JAPAN

The spectra of the squares of velocity quadratics including the energy dissipation rate epsilon per unit mass, the enstrophy omega(2) and the pressure p were measured using the data obtained from direct numerical simulations (DNSs) of incompressible turbulence in a periodic box with number of grid points up to 2048(3). These simulations were performed using the Earth Simulator computing system. The spectra for epsilon, omega(2) and p exhibited a wave number range in which the spectra scaled with the wave number k as proportional to k(-a). Exponent a for p was about 1.81, which is in good agreement with the value obtained by assuming the joint probability distribution of the velocity field to be Gaussian, while a values for epsilon and omega(2) were about 2/3, and very different from the Gaussian approximation values.

DOI： 10.1143/JPSJ.72.983

大規模DNSによる乱流物理現象の解明

金田行雄, 石原卓

日本流体力学会数値流体力学部門Web会誌 11 ( 2 ) 25-30 2003.5

Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box Reviewed

Y Kaneda, T Ishihara, M Yokokawa, K Itakura, A Uno

PHYSICS OF FLUIDS 15 ( 2 ) L21 - L24 2003.2

Language：English Publisher：AMER INST PHYSICS

High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 4096(3) grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity nu as nu-->0. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k(-5/3) scaling law, where k is the wavenumber, but the exponent is steeper than -5/3 by about 0.1. (C) 2003 American Institute of Physics.

DOI： 10.1063/1.1539855

Performance tuning of a CFD code on the earth simulator

K Itakura, A Uno, M Yokokawa, M Saito, T Ishihara, Y Kaneda

NEC RESEARCH & DEVELOPMENT 44 ( 1 ) 115 - 120 2003.1

Language：English Publisher：NEC CORP

High-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 2048(3) have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNSs based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT). In this paper, we tuned the 3D-FFT algorithm for the Earth Simulator and have achieved DNS at 16ATFLOPS on 2048(3) grid points.

Ultra Direct Numerical Simulation of Turbulence on the Earth Simulator Reviewed

Takashi Ishihara

Proc. Japan-Russia Seminar, TIT 2003

Comparison of a spectral method with a higher-order finite difference method in direct numerical simulations of three-dimensional homogeneous turbulence Reviewed

Katsunori Yoshimatsu, Takashi Ishihara, Yukio Kaneda, Satoshi Nakai, Hidetoshi Nishida, Nobuyuki Satafuka

Nippon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B 69 ( 679 ) 541 - 546 2003

Language：Japanese Publisher：Japan Society of Mechanical Engineers

A finite difference method (FDM) is easier and cheaper to use than a spectral method (SM) in flows with complicated geometry, but is inferior to a SM in both accuracy and resolution. In this paper, effects of both accuracy and resolution in a FDM on the quality of incompressible turbulent flow description were studied by comparing a SM with a FDM in direct numerical simulations (DNS) of the three-dimensional freely decaying homogeneous turbulence with 1283 and 2563 grids. We adopted the higher-order method of lines and Fourier spectral method as a FDM and a SM, respectively. The value of the kinematic viscosity was determined so that the minimum value of Kmaxη in time was about 2 in the SM with 2563 grids. Here, Kmax and η are the maximum resolved wavenumber and the Kolmogorov length scale, respectively. The statistical quantities, such as the total energy, the energy dissipation ratio, obtained by the higher-order method of lines were in good agreement with those by the SM. Furthermore, comparing their DNS fields, we found that the performance of the 4th-order method of lines with 2563 grids was comparable to that of the SM with 1283 grids in which the minimum value of Kmaxη in time was about 1.

DOI： 10.1299/kikaib.69.541

LES modelings based on the Lagrangian renormalized approximation Reviewed

K Yoshida, T Ishihara, D Fujita, T Yamahira, Y Kaneda

STATISTICAL THEORIES AND COMPUTATIONAL APPROACHES TO TURBULENCE 203 - 218 2003

Language：English Publishing type：Research paper, summary (national, other academic conference) Publisher：SPRINGER-VERLAG TOKYO

A systematic way for formulating large-eddy simulation (LES) models based on the Lagrangian renormalized approximation is presented. A spectral LES to simulate the energy spectrum and a probabilistic LES to simulate both the energy spectrum and the error spectrum are formulated for 3-dimensional turbulence and 2-dimensional turbulence with the inverse energy cascading range. The derived models axe free from any ad hoc parameters. The models are verified using high resolution numerical simulations with 512(3) grid points for 3-dimension and 1024(3) for 2-dimension.

Predictability of 3D isotropic turbulence - Effect of data assimilation Reviewed

K Hayashi, T Ishihara, Y Kaneda

STATISTICAL THEORIES AND COMPUTATIONAL APPROACHES TO TURBULENCE 239 - 247 2003

Language：English Publishing type：Research paper, summary (national, other academic conference) Publisher：SPRINGER-VERLAG TOKYO

In numerical simulation of turbulent flows, it is usually difficult to obtain exact initial conditions and it is well known that initial uncertainty in high wavenumbers spreads toward large scale through nonlinear dynamics. These imply the limitation of the numerical prediction. We present here a series of numerical experiments to study the effect of data assimilation on the predictability of isotopic 3D turbulence. In the experiment we have two parameters K-c and T to control the data assimilation, where K-c is the maximum of the assimilated wavenumber range and T is the time interval of the assimilation. It is found not only that we can suppress the growth of uncertainty by data assimilation but also that we can reduce it under appropriate conditions on K-c and T. It is also found that there exists a critical K-c* such that if K-c < K-c*, the uncertainty grows for any T.

High resolution DNS of incompressible homogeneous forced turbulence - Time dependence of the statistics Reviewed

T Ishihara, Y Kaneda

STATISTICAL THEORIES AND COMPUTATIONAL APPROACHES TO TURBULENCE 177 - 188 2003

Language：English Publishing type：Research paper, summary (national, other academic conference) Publisher：SPRINGER-VERLAG TOKYO

Results of direct numerical simulation (DNS) of incompressible homogeneous and isotropic forced turbulence with grid points up to 1024 3 are presented with emphasis on the time dependence of the turbulence statistics. The Taylor micro scale Reynolds number at a quasi-stationary state is 283 in the DNS with 1024 3 grid points, and the energy spectrum exhibits an universal equilibrium range. The results suggest that for R-lambda > 280 or so, the energy dissipation rate normalized by the integral length scale and root-mean-square velocity is almost independent of R-lambda and is 0.44 - 0.45.

LES of Stably Stratified Turbulence Reviewed

Kyo Yoshida, Takashi Ishihara, Yukio Kaneda

Proc. International Workshop on Statistical Theories and Computational Approaches to Turbulence 219-228 2002.11

Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence Reviewed

T Ishihara, Y Kaneda

PHYSICS OF FLUIDS 14 ( 11 ) L69 - L72 2002.11

Language：English Publisher：AMER INST PHYSICS

Turbulent diffusion of a pair of fluid particles in 3-dimensional homogeneous and isotropic turbulence was studied using a high-resolution direct numerical simulation (DNS) with 1024(3) grid points. The DNS showed that the mean square of the distance deltax between the two fluid particles grows with time t as <\deltax\(2)>similar toCepsilont(3) in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941), where Capproximate to0.7 and epsilon is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for <\deltax\(2)> is shown to be in good agreement with the DNS. (C) 2002 American Institute of Physics.

DOI： 10.1063/1.1508443

Scalability Evaluation of Direct Numerical Simulation on Earth Simulator

UNO ATSUYA, ITAKURA KEN'ICHI, YOKOKAWA MITSUO, ISHIHARA TAKASHI, KANEDA YUKIO

IPSJ SIG Notes 91 ( 80 ) 55 - 60 2002.8

Language：Japanese Publisher：Information Processing Society of Japan (IPSJ)

There are two programming models on the shared-memory architecure. One, called the flat programming, is using MPI, and the other, called the hybrid programming, is using MPI and shared-memory models simultaneously. In general, it is difficult that the hybrid programming outperforms the flat programming. In this study, we evaluated a scalability of large-scale direct numerical simulations of the Navier-Stokes equations on the Earth Simulator. As a result, the hybrid programming could outpeform the flat programming on the Earth Simulator. Also, we discuss the tuning strategies to obtain higher performance on the Earth Simulator.

Anisotropic velocity correlation spectrum at small scales in a homogeneous turbulent shear flow Reviewed

T Ishihara, K Yoshida, Y Kaneda

PHYSICAL REVIEW LETTERS 88 ( 15 ) 154501 - 1545014 2002.4

Language：English Publisher：AMER PHYSICAL SOC

A simple theoretical analysis and direct numerical simulations on 512(3) grid points suggest that the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number is given by a simple form that is an anisotropic function of the wave vector. The tensor is determined by the rate of the strain tensor of the mean flow, the rate of energy dissipation per unit mass, the wave vector, and two nondimensional constants.

DOI： 10.1103/PhysRevLett.88.154501

25aXB-4 Anisotropic spectrum in homogeneous shear turbulent flow

Ishihara T., Yoshida K., Kaneda Y.

Meeting abstracts of the Physical Society of Japan 57 ( 1 ) 248 - 248 2002.3

25aXB-5 Simulation of 3D homogeneous turbulence:spectral method vs. higher order method of lines

Yoshimatsu K, Ishihara T., Yamazaki Y., Kaneda Y., Nishida H., Nakai S., Satofuka N.

Meeting abstracts of the Physical Society of Japan 57 ( 1 ) 248 - 248 2002.3

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