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Indexed by:期刊论文

Date of Publication:2016-04-01

Journal:SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY

Included Journals:SCIE、EI

Volume:59

Issue:4

Page Number:1-8

ISSN No.:1674-7348

Key Words:optimal dynamical systems; weighted residual; three-dimensional Navier-Stokes equations; vortex structures

Abstract: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 multi-scale 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.