一种改进的均匀各向同性湍流初始化方法

AN IMPROVED METHOD FOR INITIALIZING HOMOGENEOUS ISOTROPIC TURBULENT FLOWS

均匀各向同性湍流是一种最简单的湍流理想状态,也是湍流基础理论研究的最重要对象之一.为了用数值方法产生均匀各向同性湍流场,一般采用Rogallo提出的方法在谱空间生成初始场,然后再转换到物理空间.研究表明,由该方法生成的初始湍流场在3个棱向上呈各向异性,在结构函数和速度概率密度分布上均有体现.尽管在初始场样本很多时,这种各向异性可以在平均意义上消除,但作为数值模拟采用的单个流场则波动较大,不利于在实际计算中作为单个初始场生成各向同性湍流.在此基础上提出一种改进的Rogallo初始化方法,称为模量平均法,将Rogallo方法在3个轴向分别进行,并进行模量平均,最后采用能谱进行模量控制.这种方法可以一方面保持初始场能谱,另一方面减小单个流场的各向异性波动,以产生各向同性程度更佳的单个初始场.在统计意义上,新方法可以分别将结构函数和速度概率密度的相对标准差减小约10%.

Homogeneous isotropic turbulence(HIT) is one of the simplest ideal turbulence states,and is also one of the most important subjects in basic turbulence theory researches.HIT fields are usually initialized in the spectrum space via the method proposed by Rogallo,and then transformed in physical space.The current paper points out that initial fields thus generated are anisotropic in axis directions of their computational domain,which can be reflected in structure functions and in possibility density distribution of velocity components.Even though such anisotropy will disappear after an average operation of a large number of initial field samples,the anisotropy fluctuation between samples is considerately big,which is not favorable for the establishment of an HIT.Basing on this existing methodology,we then proposed an improved Rogallo method,named the modulus-averaging method,which firstly conducts the Rogallo method in all the3 axis directions,then carries out a modulus-averaging operation,and finally control the modulus via a given spectrum function.This method can keep the initial filed spectrum and,reduce the anisotropy fluctuation of each single field to generate 'more isotropic' initial fields.Statistically,this new method can lower the relative standard deviations of structure functions and velocity possibility density distribution by about 10%.