Deep Learning parameterization of subgrid scales in wall-bounded turbulent flows

Abstract: An innovative \textit{deep learning} approach has been adopted to formulate the eddy-viscosity for large eddy simulation (LES) of wall-bounded turbulent flows. A deep neural network (DNN) is developed which learns to evaluate the eddy-viscosity from a dataset generated for a channel flow at friction Reynolds number $Re_{\tau} = 395$ using the Dynamic Smagorinsky subgrid-scale model. Later this DNN is employed to predict the eddy-viscosity for a number of grid configurations for channel flow at $Re_{\tau} = 395$ and $590$. The statistics computed from the DNN based LES model show an excellent match with direct numerical simulations (DNS). In some cases, particularly for the coarse grid simulations, the DNN based model yields statistics closer to DNS than those from the Dynamic Smagorinsky model. The turbulent kinetic energy budget terms also manifest a satisfactory match with the DNS results. This model computes eddy-viscosity $2-8$ times quicker than the Dynamic Smagorinsky model. This DNN based LES model is also able to closely mimic the duct flow at $Re_{\tau} = 300$ in a qualitatively and quantitatively similar manner as the LES using the Dynamic Smagorinsky model and a DNS from a previous study. This study demonstrates the feasibility of deep learning for parameterizing the subgrid-scales (SGS) in a turbulent flow accurately in a cost-effective manner. In a broader perspective, deep learning based models can be a promising alternative to traditional RANS and LES models for simulating complex turbulent flows.