Empirical eigenfunctions of transitional flow in a grooved channel are extracted by proper orthogonal decomposition (POD). POD is applied to numerical solutions of the governing Navier-Stokes partial differential equations at Reynolds numbers Re=430, 750, 1050 and at Prandtl number Pr=0.71 (air flow). For each value of Re, a low-dimensional set of nonlinear ordinary differential equations is derived by Galerkin projection. The Galerkin projection-based low-order dynamical models are used to generate the data required to efficiently train artificial neural networks in the range 400/spl les/Re/spl les/1200. Accurate artificial neural network-based models of the flow system are obtained. The study demonstrates the potential use of Galerkin projection-based and artificial neural network-based low-order models as valuable tools for flow modeling and for prediction of short- and long-term behavior of transitional flow systems. A possible real-time intelligent flow control scheme is briefly discussed.
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机译：通过适当的正交分解（POD）提取带沟槽通道中过渡流的经验特征函数。 POD应用于控制的Navier-Stokes偏微分方程的数值解，其雷诺数Re = 430、750、1050和普朗特数Pr = 0.71（空气流量）。对于Re的每个值，通过Galerkin投影推导出一个低维的非线性常微分方程组。基于Galerkin投影的低阶动力学模型用于生成有效训练400 / spl les / Re / spl les / 1200范围内的人工神经网络所需的数据。获得了基于精确人工神经网络的流动系统模型。这项研究证明了基于Galerkin投影和基于人工神经网络的低阶模型作为流动模型以及预测过渡流动系统的短期和长期行为的有价值的工具的潜在用途。简要讨论了可能的实时智能流控制方案。
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