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Construction of reduced-order models for fluid flows using deep feedforward neural networks

Published online by Cambridge University Press:  14 June 2019

Hugo F. S. Lui  and
William R. Wolf Open the ORCID record for William R. Wolf [Opens in a new window]
Hugo F. S. Lui
Affiliation:
School of Mechanical Engineering, Universidade Estadual de Campinas, Campinas, SP13083-860, Brazil
William R. Wolf*
Affiliation:
School of Mechanical Engineering, Universidade Estadual de Campinas, Campinas, SP13083-860, Brazil
*
†Email address for correspondence: wolf@fem.unicamp.br
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Abstract

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

JFM classification

Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Low-dimensional models

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 872 , 10 August 2019 , pp. 963 - 994
Copyright
© 2019 Cambridge University Press 

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Lui and Wolf supplementary movie 1

Movie showing x-momentum for full and reduced order models (cylinder flow)

Download Lui and Wolf supplementary movie 1(Video)
Video 9.3 MB

Lui and Wolf supplementary movie 2

Movie showing Q-criterion colored by pressure for full and reduced order models (3D flow of plunging airfoil)

Download Lui and Wolf supplementary movie 2(Video)
Video 49.4 MB

Lui and Wolf supplementary movie 3

Movie showing x-momentum for full and reduced order models (spanwise-averaged flow of plunging airfoil)

Download Lui and Wolf supplementary movie 3(Video)
Video 12.1 MB