Reynolds stress correction by data assimilation methods with physical constraints

Reynolds-averaged Navier-Stokes (RANS) models are extensively employed in industrial settings for the purpose of simulating intricate fluid flows. However, these models are subject to certain limitations. Notably, disparities persist in the Reynolds stresses when comparing the RANS model with high-fidelity data obtained from Direct Numerical Simulation (DNS) or experimental measurements. In this work we propose an approach to mitigate these discrepancies while retaining the favorable attributes of the Menter Shear Stress Transport (SST) model, such as its significantly lower computational expense compared to DNS simulations. This strategy entails incorporating an explicit algebraic model and employing a neural network to correct the turbulent characteristic time. The imposition of realizability constraints is investigated through the introduction of penalization terms. The assimilated Reynolds stress model demonstrates good predictive performance in both in-sample and out-of-sample flow configurations. This suggests that the model can effectively capture the turbulent characteristics of the flow and produce physically realistic predictions.