A Two Neural Network Subgrid Stress Model for Large Eddy Simulation*

A spatial 3D Unet Convolutional Neural Network based on a tensor basis expansion of the subgrid stress tensor is designed to combine multi-scale features of turbulence while enforcing the subgrid stress tensor structure. A novel two neural network variant of this design is applied to predict the structure and the magnitude of the subgrid stress tensor separately, with a loss function that enforces physical quantities related to the subgrid stress tensor. The two neural network variant is analyzed in a priori and a posteriori settings with large eddy simulations of Forced Homogeneous Isotropic Turbulence and Channel Flow conditions. In an a priori setting, it is demonstrated that the two neural network concept is able to accurately predict the subgrid stress even when over 50 percent of the total energy (as compared to Direct Numerical Simulation) is filtered out and is an improvement over a one neural network concept. By training on different filter widths with varying size inputs, the neural network is shown to generalize to an intermediate filter width. Turbulent space-time correlations in a posteriori analysis are also conducted and compared with current subgrid stress models.