| Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析 |
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| 引用本文： | 王金城,齐进,吴锤结.Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析[J].应用数学和力学,2020(3):235-249. |
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| 作者姓名： | 王金城 齐进 吴锤结 |
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| 作者单位： | 大连理工大学航空航天学院;北京应用物理与计算数学研究所 |
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| 基金项目： | 国家自然科学基金(11601033,11372068);国家重点基础研究发展计划(973计划)(2014CB744104)。 |
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| 摘 要： | 研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题,并基于双尺度全局最优化方法,建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加,双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.
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| 关 键 词： | 脉动速度方程 最优动力系统 分岔特性 双方柱绕流 |
Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations |
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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(3):235-249. |
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| Authors: | WANG Jincheng QI Jin WU Chuijie |
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| Institution: | (School of Aeronautics and Astronautics,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China;Institute of Applied Physics and Computational Mathematics,Beijing 100088,P.R.China) |
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| 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 Poincarésection,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. |
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| Keywords: | fluctuation velocity equation dynamical system bifurcation flow around two square columns |
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