Analysis and Modelling of Optimal Dynamical Systems of Incompressible NavierStokes Equations

WANG Jincheng; QI Jin; WU Chuijie

doi:10.21656/1000-0887.400279

Volume 41 Issue 1

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WANG Jincheng, QI Jin, WU Chuijie. Analysis and Modelling of Optimal Dynamical Systems of Incompressible NavierStokes Equations[J]. Applied Mathematics and Mechanics, 2020, 41(1): 1-15. doi: 10.21656/1000-0887.400279

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Analysis and Modelling of Optimal Dynamical Systems of Incompressible NavierStokes Equations

doi: 10.21656/1000-0887.400279

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 Basic Research Program of China(973 Program)(2014CB744104)

Received Date: 2019-09-06
Rev Recd Date: 2019-11-26
Publish Date: 2020-01-01

Abstract

Abstract

The modeling method for the optimal dynamical systems of NavierStokes equations satisfying both arbitrary velocity boundary conditions and velocity incompressible conditions was studied. Through the modeling and analysis of the optimal dynamical systems of the flow around the square column, it is found that the dynamics characteristics of the optimal dynamical systems are limit cycles. At the same time, the optimal dynamical system with only 3 optimal basis functions could well describe all the main flow field characteristics and the dynamics characteristics of the problem, so the proposed method is applicable to complex flow problems and their dynamics with minimal basis functions.
- optimization,
- dynamical system,
- 3D NavierStokes equation,
- dynamics characteristics

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References

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