New methodologies for machine learning assisted turbulence based on the transport equations for the Reynolds stress tensor and the Reynolds force vector

Abstract

The long lasting demand for better turbulence models and the still prohibitively computational cost of high- delity uid dynamics simulations, like DNS and LES, have led to a rising interest in coupling available high- delity datasets and popular, yet poor, RANS simulations through Machine Learning techniques. These techniques use noble sources as training targets for predicting quantities to be propagated by RANS equations. Many of the recent advances used the Reynolds stress tensor as the target for these corrections. More recently, an alternate methodology used the divergence of the Reynolds stress, denominated the Reynolds Force Vector, computed indirectly by manipulating mean momentum balance, as the target for the Machine Learning techniques. An unexplored strategy in this e ort is to use transport equations for turbulent quantities fueled by Machine Learning predicted source terms. In this context, two new methodologies were proposed, one using a transport equation for the Reynolds Stress and another one using a transport equation for the Reynolds Force Vector. The combination of these transport equations along with the momentum balance and a pressure coupling formed two data-driven turbulence models. Neural Networks were trained using DNS data to predict the source terms of each equation. Subsequently, both proposed models were employed to correct the turbulent ow on a square-duct. Reasonable results were obtained by both datadriven turbulence models, consistently recovering the secondary ow on the duct, which was not present in the baseline simulations that used the κ - model. Results from both methods were compared with alternate strategies previously presented in literature.