基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法

LMS Method:a Spatiotemporal Optimal Low-Dimensional Dynamical Systems of Multi-Scale Numerical Simulation Method for Compressible Turbulence

按照周培源教授关于研究湍流数值模拟建模时必须分析和求解脉动速度场的思想,该研究基于第一性原理,系统地建立了基于时空低维最优动力系统的多尺度可压缩湍流数值模拟方法(LMS方法),并将其应用于多次冲击Richtmyer-Meshkov问题的数值模拟中,首次得到了可压缩湍流的中尺度流场和不同于DNS近似解的湍流近似解.数值结果表明,LMS方法可以用较少的网格获得更精确的湍流近似解.首先解决了研究中遇到的几个问题,为LMS方法的构建铺平了道路.这些问题是:基于湍流的物理特性,提出了湍流大、中、小尺度分解的新概念;找到了box滤波空间相关性的计算方法;指出了湍流建模理论中长期存在的逻辑错误,提出了多尺度湍流模型的概念;讨论了湍流封闭问题的本质和关键,给出了克服湍流封闭问题的数值方法.采用box滤波方法/空间网格平均方法且在大尺度网格的意义下,LMS方法的本质是一种将RANS、LES、DES和DNS等湍流数值模拟方法统一的全新湍流数值模拟方法.需要指出的是,LMS方法也可以作为湍流模型研究的辅助工具,以检验SGS尺度方程/脉动方程中各项所对应的湍流模型是否正确.

Following Professor P-Y CHOU’s idea,i.e.,to study numerical simulation of turbulence,it is necessary to analyse and solve the fluctuating velocity field,based on the first principles,the spatiotemporal low-dimensional optimal dynamical systems of multi-scale simulation method(LMS method)is established systematically in this work,and in its application to the numerical simulation of re-shock Richtmyer-Meshkov problem,the turbulent middle-scale flow field and an approximate solution of turbulence which is different from the DNS approximate solution of turbulence,are obtained for the first time;the numerical results show that LMS method can be used with fewer grids to obtain more accurate approximate solutions of turbulence.Several problems encountered in the research are solved first,which paved the road to construct LMS method.These problems are:based on the physical characteristics of turbulence,a new concept of large,middle and small scale decomposition of turbulence is proposed;calculation method of spatial correlation of box filtering is find;a long-standing logical error in the theory of turbulence modelling is pointed out and the concept of multi-scale turbulence models is suggested;essence and key of closure problem of turbulence are discussed and numerical method for overcoming the closure problem of turbulence is given.With the box filtering/the space grid average and in the sense of a large-scale grid,the essence of the LMS method is a new turbulence numerical simulation method that integrates the RANS,LES,DES and DNS.It is necessary to indicate that the LMS method can also serve as an auxiliary tool for turbulence model research to examine whether the turbulence model corresponding to each term in the SGS-scale/fluctuations equation is correct or not.