Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear Operators
Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear Operators
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基于线性算子谱分析的计算水动力稳定性和流量控制
DOI：
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发表时间：
2012
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通讯作者：
S. Bagheri
中科院分区：
文献类型：
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作者：
S. Bagheri
本文考虑使用动力系统和控制理论的工具来分析和控制流体流动。所使用的工具源自与纳维-斯托克斯方程相关的各种线性算子的谱分析。线性化纳维-斯托克斯算子、库普曼算子、空间相关算子和汉克尔算子的谱分解提供了一种对复杂流的动力学进行物理洞察的方法，并能够构建适合控制设计的低维模型。由于纳维-斯托克斯方程的离散化通常会导致非常大规模的动力系统，因此必须采用无矩阵技术以及在某些情况下的迭代技术来解决特征值问题。数值算法的共同主题是使用直接数值模拟。该理论和算法以平板上的流动和横流中的射流为例，作为层流-湍流转变和三维涡旋脱落的原型。
This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory. The employed tools are derived from the spectral analysis of various linear operators associated with the Navier–Stokes equations. Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provide a means to gain physical insight into the dynamics of complex flows and enables the construction of low-dimensional models suitable for control design. Since the discretization of the Navier-Stokes equations often leads to very large-scale dynamical systems, matrix-free and in some cases iterative techniques have to be employed to solve the eigenvalue problem. The common theme of the numerical algorithms is the use of direct numerical simulations. The theory and the algorithms are exemplified on flow over a flat plate and a jet in crossflow, as prototypes for the laminar-turbulent transition and three-dimensional vortex shedding.