Optimal mode decomposition for unsteady flows
Optimal mode decomposition for unsteady flows
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DOI：
10.1017/jfm.2013.426
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发表时间：
2013-09
影响因子：
3.7
通讯作者：
A. Wynn;D. Pearson;B. Ganapathisubramani;P. Goulart
中科院分区：
文献类型：
--
作者：
A. Wynn;D. Pearson;B. Ganapathisubramani;P. Goulart
摘要提出了一种求解流体流动演化的线性模型的新方法——最优模态分解（OMD）。该方法估计了一个高维系统的线性动力学，该系统首先被投影到一个用户定义的固定秩的子空间上。采用迭代法求线性模型与子空间的最优组合，使系统残差最小。证明了OMD方法是动态模态分解（DMD）的推广，其中子空间不是优化而是固定为适当的正交分解（POD）模态。此外，证明了OMD提供了对底层系统的库普曼模态和特征值的近似。利用合成波形和实验数据集对OMD和DMD进行了比较。OMD技术被证明具有比DMD更低的残余误差，并且显示在合成波形上，以提供更准确的系统特征值估计。这种新方法可以与实验和数值数据一起使用，以计算具有用户定义等级的“最佳”低阶模型，该模型最能捕获非定常和湍流的系统动力学。
Abstract A new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal’ low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flows.