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。我们具有理论上和数值的研究性密度密度函数（PDF）Q（PDF）Q（ξ）的速度梯度ξ=ξ=ξθU/θx在强制的一个维汉堡方程中，该方程众所周知，它是Navier-Stokes湍流的简单模型，以及用于随机接口的模型的模型。发现Q（ξ）非常偏斜，具有代数尾巴，然后对大负负ξ.2的指数减小。我们已经使用高性能矢量并行机器（Fujitsu VPP5000）在Nagoya University使用高性能矢量平行机（Fujitsu VPP5000）进行了非常大的3D不可压缩湍流DNS。为此，已经为平行机开发了非常有效的FFT。在分辨率n = 1024 D13 D1的情况下，我们已将Raynolds编号RIYD2λD2= 490，目前最高值和世界记录，并获得了各种值得注意的发现。结果很快就在ITP，UCSB的国际动荡会议上进行了讨论，并吸引了观众的浓厚兴趣（http://online.itp.ucsb.edu/online/hydrot_c00).3。给定值的ΔU（r）= u（x+r）-u（x）的navier-stokes方程的耗散项的物理或条件平均值使我们对PDF Q（ΔU）有一些见解。发现3D稳定同质湍流中Q（ΔU）的不对称形式对于小|ΔU|除了大|ΔU|的预偏和指数外，它与dns.4非常吻合。我们已经检查了DNS中压力及其梯度的差异。发现他们的价值和雷诺数依赖性与经典的科尔莫戈罗夫理论所预测的价值观不同。差异可以用压力的泊松方程中的源项的连贯结构来解释。还发现了压力谱的新缩放。重要发现之一是kolmogorov缩放中压力谱的通用常数为4.48。