Investigation of nonlocal data-driven methods for subgrid-scale stress modeling in large eddy simulation

A nonlocal subgrid-scale stress (SGS) model is developed based on the convolution neural network (CNN), which is a powerful supervised data-driven method and also an ideal approach to naturally consider spatial information due to its wide receptive field. The CNN-based models used in this study take primitive flow variables as input only, and then, the flow features are automatically extracted without any a priori guidance. The nonlocal models trained by direct numerical simulation (DNS) data of a turbulent channel flow at Reτ = 178 are accessed in both the a priori and a posteriori tests, providing reasonable flow statistics (such as mean velocity and velocity fluctuations) close to the DNS results even when extrapolating to a higher Reynolds number Reτ = 600. It is identified that the nonlocal models outperform local data-driven models, such as the artificial neural network, and some typical SGS models (e.g., the dynamic Smagorinsky model) in large eddy simulation (LES). The model is also robust with stable numerical simulation since the solutions can be well obtained when examining the grid resolution from one-half to double of the spatial resolution used in training. We also investigate the influence of receptive fields and propose using the two-point correlation analysis as a quantitative method to guide the design of nonlocal physical models. The present study provides effective data-driven nonlocal methods for SGS modeling in LES of complex anisotropic turbulent flows.