不可压缩Navier-Stokes方程最优动力系统建模和分析  

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

作　　者：王金城 齐进[2] 吴锤结[1] WANG Jincheng;QI Jin;WU Chuijie(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)

机构地区：[1]大连理工大学航空航天学院,辽宁大连116024 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《应用数学和力学》2020年第1期1-15,共15页Applied Mathematics and Mechanics

基　　金：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)~~

摘　　要：研究了同时满足任意速度边界条件和速度不可压条件的Navier-Stokes方程最优动力系统的建模方法.通过对方柱绕流问题的最优动力系统的建模与分析,发现该最优动力系统的动力学特性为极限环.同时,该最优动力系统仅使用了三个最优基函数就很好地描述了所有主要的流场特征和该问题的动力学特性,故满足任意速度边界条件和速度不可压条件Navier-Stokes方程最优动力系统的建模方法,能够用最少的基函数最大限度地描述复杂流体问题及其动力学特性.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 a-round 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 char-acteristics of the problem,so the proposed method is applicable to complex flow problems and their dynamics with minimal basis functions.

关 键 词：最优化 动力系统 三维不可压缩Navier-Stokes方程 动力学特性 

分 类 号：O357.41[理学—流体力学]