Deep learning of subfilter-scale turbulence for large eddy simulation*

High-fidelity fluid dynamics simulations, namely, Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES), are computationally expensive for high Reynolds number problems. Although Reynolds Averaged Navier-Stokes (RANS) methods have shown qualified success for such flows, many aspects such as heat transfer rates are poorly reproduced, while others such as unsteadiness are outside their purview. Hybrid RANS/LES methods provide a middle ground depending on the scale and required fidelity. As the scope of problems grows larger, it is imperative that new techniques and methods are developed to extend modeling capabilities and improve the efficiency of calculation. To this end, we implement Convolutional Neural Networks (CNN) that learn the features of subfilter-scale turbulence in higher resolution simulations and augment the fidelity of lower resolution simulations, utilizing the highly parallel nature of neural networks to efficiently predict future results. Moreover, we introduce a recurrent training paradigm to stabilize predictions and encourage the consistency of future results. The case studies comprise a lid-driven cavity at Mach 0.5 and a supersonic (Mach 2.7) shock boundary layer interaction. Testing of a variety of neural network architectures ranging from shallow CNNs to popular deep ResNet and U-Net setups as well as Generative Adversarial Networks (GAN) indicate that the models are capable of accurately predicting future timesteps, but only for relatively short time durations. The results enforce the need to explicitly encode physics information into machine learning models. By incorporating physical constraints and partial differential equation information into the models, we anticipate greater stability in the training process and the delivery of an efficient and accurate method for subfilter-scale turbulence modeling.