Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data
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Recently, the methodology of deep learning is used to improve the calculation accuracy of the Reynolds-averaged Navier-Stokes (RANS) model. In this paper, a neural network is designed to predict the Reynolds stress of a channel flow of different Reynolds numbers. The rationality and the high efficiency of the neural network is validated by comparing with the results of the direct numerical simulation (DNS), the large eddy simulation (LES), and the deep neural network (DNN) of other studies. To further enhance the prediction accuracy, three methods are developed by using several algorithms and simplified models in the neural network. In the method 1, the regularization is introduced and it is found that the oscillation and the overfitting of the results are effectively prevented. In the method 2, y+ is embedded in the input variable while the combination of the invariants is simplified in the method 3. From the predicted results, it can be seen that by using the first two methods, the errors are reduced. Moreover, the method 3 shows considerable advantages in the DNS trend and the smoothness of a curve. Consequently, it is concluded that the DNNs can predict effectively the anisotropic Reynolds stress and is a promising technique of the computational fluid dynamics.
Key wordsDeep neural network channel flow turbulence model Reynolds stress
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- Feiereisen W. J. Numerical simulation of a compressible homogeneous, turbulent shear flow [D]. Doctoral Thesis, Stanford, USA: Stanford University, 1981.Google Scholar
- Speziale C. G. A review of Reynolds stress models for turbulent shear flows [C]. 20th Symposium on Naval Hydrodynamics, Washington DC, USA, 1995.Google Scholar
- Tracey B., Duraisamy K., Alonso J. Application of supervised learning to quantify uncertainties in turbulence and combustion modeling [C]. 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Texas, USA, 2013, 2013–0259.Google Scholar
- Wang J. X., Wu J. L., Xiao H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data [J]. Physical Review Fluids, 2017, 2(3): 1–22.Google Scholar
- Jarrett K., Kavukcuoglu K., Ranzato M. et al. What is the best multi-stage architecture for object recognition? [C]. International Conference on Computer Vision (ICCV), Kyoto, Japan, 2009, 2146–2153.Google Scholar
- Krizhevsky A., Sutskever I., Hinton G. E. ImageNet classification with deep convolutional neural networks [C]. 25th International Conference on Neural Information Processing Systems, Nevada, USA, 2012, 1097–1105.Google Scholar
- He K., Zhang X., Ren S. et al. Deep residual learning for image recognition [C]. International Conference on Computer Vision (ICCV), Santiago, Chile, 2015, 1026–1034.Google Scholar
- Maas A. L., Hannun A. Y., Ng A. Y. Rectifier nonlinearities improve neural network acoustic models [C]. International Conference on Machine Learning (ICML), Atlanta, USA, 2013.Google Scholar
- Krogh A., Hertz J. A. A simple weight decay can improve generalization [C]. International Conference on Neural Information Processing Systems. San Mateo, California, USA, 1992, 950–957.Google Scholar