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

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.