An artificial neural network model for recovering small-scale velocity in large-eddy simulation of isotropic turbulent flows

Small-scale motions in turbulent flows play a significant role in various small-scale processes, such as particle relative dispersion and collision, bubble or droplet deformation, and orientation dynamics of non-sphere particles. Recovering the small-scale flows that cannot be resolved in large eddy simulation (LES) is of great importance for such processes sensitive to the small-scale motions in turbulent flows. This study proposes a subgrid-scale model for recovering the small-scale turbulent velocity field based on the artificial neural network (ANN). The governing equations of small-scale turbulent velocity are linearized, and the pressure gradient and the nonlinear convection term are modeled with the aid of the ANN. Direct numerical simulation (DNS) and filtered direct numerical simulation (FDNS) provide the data required for training and validating the ANN. The large-scale velocity and velocity gradient tensor are selected as inputs for the ANN model. The linearized governing equations of small-scale turbulent velocity are numerically solved by coupling the large-scale flow field information. The results indicate that the model established by the ANN can accurately recover the small-scale velocity lost in FDNS due to filtering operation. With the ANN model, the flow fields at different Reynolds numbers agree well with the DNS results regarding velocity field statistics, flow field structures, turbulent energy spectra, and two-point, two-time Lagrangian correlation functions. This study demonstrates that the proposed ANN model can be applied to recovering the small-scale velocity field in the LES of isotropic turbulent flows at different Reynolds numbers.