Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations

WANG Jincheng; QI Jin; WU Chuijie

doi:10.21656/1000-0887.400277

Volume 41 Issue 3

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WANG Jincheng, QI Jin, WU Chuijie. Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2020, 41(3): 235-249. doi: 10.21656/1000-0887.400277

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Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations

doi: 10.21656/1000-0887.400277

¹School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;²Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R.China

Funds: The National Natural Science Foundation of China(11601033; 11372068); The National Key Basic Research Program of China (973 Program)(2014CB744104)

Received Date: 2019-09-06
Rev Recd Date: 2020-01-10
Publish Date: 2020-03-01

Abstract

Abstract

The modelling theory of the optimal low-dimensional dynamical system of the fluctuation velocity equations of the Navier-Stokes equations was studied. The optimal target functional is the incompressibility and orthogonality of the fluctuation velocity basis function. The fully developed side-by-side two-column flow problem was numerically simulated. Based on the two-scale global optimization method, the optimal dynamical system model for its fluctuation velocity was established. The dynamics properties of the phase portraits, the Poincaré section, the bifurcation characteristics, the power spectrum and the Lyapunov exponent set were analyzed. With the increase of the Reynolds number, the optimal dynamical systems of the fluctuation velocity equations of the flow around the two columns exhibit complex quasi-periodic bifurcation behaviors.
- fluctuation velocity equation,
- dynamical system,
- bifurcation,
- flow around two square columns

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References(11)

References

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