Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation

Abstract

Data-driven machine learning algorithms, random forests and artificial neural network (ANN), are used to establish the subgrid-scale (SGS) model for large-eddy simulation. A total of 30 flow variables are examined as the potential input features. A priori tests indicate that the ANN algorithm provides a better solution for this regression problem. The relative importance of the input variables is evaluated by the two algorithms. It reveals that the gradient of filtered velocity and the second derivative of filtered velocity account for a vast majority of the importance. Besides, a pattern is found for the dependence of each component of the SGS stress tensor on the input features. Accordingly, a new uniform ANN model is proposed to provide closure for all the components of the SGS stress, and a correlation coefficient over 0.7 is reached. The proposed new model is tested by large-eddy simulation of isotropic turbulence. By examining the energy budget and the dissipative properties, the ANN model shows good agreement with direct numerical simulation and it provides better predictions than the Smagorinsky model and the dynamic Smagorinsky model. The current research suggests that data-driven algorithms are effective approaches to help us discover knowledge from large amounts of data.