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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.本文从理论上和数值上研究了一维受迫Burgers方程中速度梯度的概率密度函数（PDF）Q（θx），该方程是一个简单的Navier-Stokes湍流模型，也是一个随机界面增长模型。研究发现，Q（λ）是非常偏斜的，并且具有代数尾，当λ为大负值时，Q（λ）呈指数下降.我们在名古屋大学用32个处理器的高性能矢量并行机（Fujitsu VPP 5000）进行了非常大规模的三维不可压缩湍流的DNS。一个非常有效的FFT的并行机已开发用于此目的。在分辨率为N = 1024 × 10 ~（13）× 10 ~（这些结果很快就在ITP，UCSB的湍流国际会议上发表，并引起了听众的强烈兴趣（http：//online.itp.ucsb.edu/online/hydrot_c00）。对于给定的δu（r）= u（x+r）-u（x），Navier-Stokes方程的耗散项的物理或条件平均值给了我们一些关于PDf Q（δu）的见解。在三维定常均匀湍流中，当湍流强度较小时，Q（δu）的渐近形式为高斯型。|δu|除了大的前因子和指数|δu|，与DNS协议一致。本文用DNS方法研究了三维均匀湍流中压力及其梯度的变化。结果表明，它们的值和雷诺数的依赖性是不同的经典Kolmogorov理论预测的。这种差异可以用压力泊松方程中源项的相干结构来解释。还发现了一个新的压力谱标度。其中一个重要的发现是在柯尔莫哥洛夫尺度下的压力谱的普适常数为4.48。