Probability distribution function and parallel numerical simulation in turbulence

湍流中的概率分布函数和并行数值模拟

基本信息

批准号：
09640260
负责人：
GOTOH Toshiyuki
金额：
$ 1.98万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640260/
关键词：
turbulence DNS Burgers spectrum parallel machine FFT pressure Probability density function 並列化確率分布関数並列計算

项目摘要

1. We have theoretically and numerically studied probability density function (PDF) Q(ξ) for the velocity gradient ξ =Ξ θu/θx in the forced one dimensional Burgers equation which is well known as a simple model for the Navier-Stokes turbulence as well as a model for the growth of random interface. It is found that Q(ξ) is very skewed and has an algebraic tail followed by the exponential decrease for large negative ξ.2. We have performed very large scale DNSs of the 3D incompressible turbulence using high performance vector parallel machine (Fujitsu VPP5000) with 32 processors at Nagoya University. A very efficient FFT for the parallel machine has been developed for this purpose. With the resolution N = 1024ィイD13ィエD1, we have attained the Raynolds number RィイD2λィエD2 = 490, the highest value and world record at present, and obtained various notable findings. The results have soon been talked at the international conference on turbulence at ITP, UCSB, and attracted very strong interests of the audience (http://online.itp.ucsb.edu/online/hydrot_c00).3. Physics or conditional averages of the dissipation term of the Navier-Stokes equation for a given value of δu(r) = u(x+r)-u(x) gives us some insights into the PDf Q(δu). Asymptotic forms of Q(δu) in 3D steady homogenous turbulence are found to be Gaussian for small |δu| except prefactor and exponential for large |δu|, which is in good agreement with DNS.4. We have examined the variances of the pressure and its gradient in the 3D homogenous turbulence by the DNS. It is found that their values and Reynolds number dependence are different from the ones predicted by classical Kolmogorov theory. The difference can be explained in terms of the coherent structure of the source term in the Poisson equation for the pressure. Also found is a new scaling for the pressure spectrum. One of the important findings is a universal constant of the pressure spectrum in the Kolmogorov scaling as 4.48.

1. 我们从理论上和数值上研究了强制一维 Burgers 方程中速度梯度 xi =Ξ θu/θx 的概率密度函数 (PDF) Q(xi)，该方程是众所周知的纳维-斯托克斯湍流的简单模型：以及随机界面增长的模型，我们发现 Q(xi) 非常偏斜，并且具有代数尾部，并且对于大的负 xi.2 呈指数下降。为此，名古屋大学使用具有 32 个处理器的高性能矢量并行机（Fujitsu VPP5000）执行了 3D 不可压缩湍流的超大规模 DNS。我们已经达到了雷诺数R2D2D2 = 490，这是当时的最高值和世界纪录并获得了各种值得注意的发现，很快就在 ITP、UCSB 的国际湍流会议上进行了讨论，并引起了观众的强烈兴趣（http://online.itp.ucsb.edu/online/Hydrot_c00）。 .3. 对于给定值 δu(r) = u(x+r)-u(x) 的纳维-斯托克斯方程耗散项的物理或条件平均值让我们对以下内容有了一些了解PDf Q(δu) 在 3D 稳态均匀湍流中，除了前因子和大 |δu| 的指数外，Q(δu) 的渐近形式被发现是高斯的，这与 DNS.4 非常一致。通过 DNS 检查了 3D 均匀湍流中的压力及其梯度的方差，发现它们的值和雷诺数依赖性与经典 Kolmogorov 预测的不同。理论中的差异可以用压力泊松方程中的源项的相干结构来解释。重要的发现之一是压力谱的通用常数。柯尔莫哥洛夫标度为 4.48。