Artificial Neural Network Modeling Small-Scale Turbulence of Isotropic Turbulent Flows

Small-scale fluid motions play an important role in the relative dispersion and clustering of inertial particles in turbulent flows. In this paper, an artificial neural network (ANN) is used to recover the small-scale turbulence of isotropic turbulent flows in the context of a prior large-eddy simulation (LES). The nonlinear convection and pressure gradient terms in the governing equations of subgrid-scale (SGS) velocity are treated as output labels \({C}_{i}\) , and the large-scale velocity and the velocity gradient tensor are taken as input features. The data required for training and testing of the ANN are provided by the Direct Numerical Simulation (DNS) and filtered Direct Numerical Simulation (FDNS). The optimized model highly fits the relationship between input features and output labels. Using the ANN model and large-scale flow field information, the approximate governing equation of small-scale motions is solved numerically, and the small-scale flow field can be obtained. The developed flow field can be statistically consistent with the results of DNS. The probability density function (PDF) of small-scale velocity and velocity gradient tensor are consistent with those of DNS. Our research indicates that the small-scale flow field can be calculated by combining the large-scale flow field with the ANN methods. Furthermore, we combine the ANN model with FDNS to predict the statistics of heavy particles as a prior LES. The results show that the a prior LES with ANN model can improve the prediction accuracy in clustering and relative velocity of particle pairs. This study provides a feasible method for constructing small-scale turbulence, which can reduce the amount of computation compared with DNS and used to the study of small-scale turbulent mixing.