Physics-guided deep learning for generating turbulent inflow conditions

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In this paper, we propose an efficient method for generating turbulent inflow conditions based on deep neural networks. We utilise the combination of a multiscale convolutional auto-encoder with a subpixel convolution layer ( ${\rm MSC}_{\rm {SP}}$ -AE) and a long short-term memory (LSTM) model. Physical constraints represented by the flow gradient, Reynolds stress tensor and spectral content of the flow are embedded in the loss function of the ${\rm MSC}_{\rm {SP}}$ -AE to enable the model to generate realistic turbulent inflow conditions with accurate statistics and spectra, as compared with the ground truth data. Direct numerical simulation (DNS) data of turbulent channel flow at two friction Reynolds numbers $Re_{\tau } = 180$ and 550 are used to assess the performance of the model obtained from the combination of the ${\rm MSC}_{\rm {SP}}$ -AE and the LSTM model. The model exhibits a commendable ability to predict instantaneous flow fields with detailed fluctuations and produces turbulence statistics and spectral content similar to those obtained from the DNS. The effects of changing various salient components in the model are thoroughly investigated. Furthermore, the impact of performing transfer learning (TL) using different amounts of training data on the training process and the model performance is examined by using the weights of the model trained on data of the flow at $Re_{\tau } = 180$ to initialise the weights for training the model with data of the flow at $Re_{\tau } = 550$ . The results show that by using only 25% of the full training data, the time that is required for successful training can be reduced by a factor of approximately 80% without affecting the performance of the model for the spanwise velocity, wall-normal velocity and pressure, and with an improvement of the model performance for the streamwise velocity. The results also indicate that using physics-guided deep-learning-based models can be efficient in terms of predicting the dynamics of turbulent flows with relatively low computational cost.