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

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• 作者：NaiFu Peng ; Hui Guan ; ChuiJie Wu
• 关键词：optimal dynamical systems ; weighted residual ; three ; dimensional Navier ; Stokes equations ; vortex structures
• 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：59
• 期：4
• 全文大小：1,534 KB
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• 作者单位：NaiFu Peng (1) (2)
  Hui Guan (3)
  ChuiJie Wu (1)
  
  1. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, 116024, China
  2. State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing, 100871, China
  3. College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing, 211101, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Chinese Library of Science
  Mechanics, Fluids and Thermodynamics
  Physics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1927

文摘

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.