Dynamic Mode Decomposition for Large-Scale Coherent Structure Extraction in Shear Flows
Dynamic Mode Decomposition for Large-Scale Coherent Structure Extraction in Shear Flows
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DOI：
10.1109/tvcg.2021.3124729
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发表时间：
2021-11
影响因子：
5.2
通讯作者：
Duong B. Nguyen;Panruo Wu;R. O. Monico;Guoning Chen
中科院分区：
文献类型：
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作者：
Duong B. Nguyen;Panruo Wu;R. O. Monico;Guoning Chen
剪切流是流体在两个不同速度运动的表面之间产生的，在许多剪切流中都观察到了大尺度结构。更好地理解剪切流中结构（尤其是大尺度结构）的物理特性，将有助于解释各种物理现象，并提高我们对更复杂湍流的建模能力。为了捕获这样的结构，已经做出了许多努力;然而，常规方法有其局限性，例如参数选择的任意性或对某些设置的特异性。为了解决这一挑战，我们建议使用多分辨率动态模式分解（mrDMD），剪切流中的大规模结构提取。特别是，我们表明，慢动作DMD模式能够揭示剪切流中的大尺度结构，也有缓慢的动态。在大多数情况下，我们发现，最慢的DMD模式和它的重建流可以充分捕捉剪切流中的大尺度动力学，这导致了一个参数的大尺度结构提取的策略。然后，借助于最慢的DMD模式，可以产生大尺度结构的有效可视化。为了加快mrDMD的计算速度，我们提供了一个快速的基于GPU的实现。我们还将我们的方法应用到一些非剪切流，不需要表现出准线性，以证明我们的策略的限制，使用最慢的DMD模式。对于非剪切流，我们表明，从不同层次的mrDMD的多个模式可能需要充分表征的流动行为。
Large-scale structures have been observed in many shear flows which are the fluid generated between two surfaces moving with different velocity. A better understanding of the physics of the structures (especially large-scale structures) in shear flows will help explain a diverse range of physical phenomena and improve our capability of modeling more complex turbulence flows. Many efforts have been made in order to capture such structures; however, conventional methods have their limitations, such as arbitrariness in parameter choice or specificity to certain setups. To address this challenge, we propose to use Multi-Resolution Dynamic Mode Decomposition (mrDMD), for large-scale structure extraction in shear flows. In particular, we show that the slow-motion DMD modes are able to reveal large-scale structures in shear flows that also have slow dynamics. In most cases, we find that the slowest DMD mode and its reconstructed flow can sufficiently capture the large-scale dynamics in the shear flows, which leads to a parameter-free strategy for large-scale structure extraction. Effective visualization of the large-scale structures can then be produced with the aid of the slowest DMD mode. To speed up the computation of mrDMD, we provide a fast GPU-based implementation. We also apply our method to some non-shear flows that need not behave quasi-linearly to demonstrate the limitation of our strategy of using the slowest DMD mode. For non-shear flows, we show that multiple modes from different levels of mrDMD may be needed to sufficiently characterize the flow behavior.