Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual  

作　　者：NaiFu Peng Hui Guan ChuiJie Wu 

机构地区：[1]State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics,Dalian University of Technology [2]State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology,College of Engineering, Peking University [3]College of Meteorology and Oceanography, PLA University of Science and Technology

出　　处：《Science China(Physics,Mechanics & Astronomy)》2016年第4期78-85,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11372068 and 11572350);the National Basic Research Program of China(Grant No.2014CB744104)

摘　　要：In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu ＆ Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

关 键 词：optimal dynamical systems weighted residual three-dimensional Navier-Stokes equations vortex structures 

分 类 号：O175[理学—数学]