Physics-Informed Machine Learning for Predictive Turbulence Modeling: Towards a Complete Framework

Abstract

Although increased availability of computational resources has enabled high-fidelity simulations (e.g., large eddy simulations) of turbulent flows, the Reynolds-Averaged Navier–Stokes (RANS) models are still the dominant tools in industrial applications. However, the predictive capabilities of RANS models are limited by large model-form discrepancies due to the Reynolds stress closure. Recently, a Physics-Informed Machine Learning (PIML) approach has been proposed to learn the functional form of Reynolds stress discrepancy in RANS simulations based on available data. It has been demonstrated that the learned discrepancy function can be used to improve Reynolds stresses in new flows where data are not available. However, due to a number of challenges, the improvements are only demonstrated in the Reynolds stress prediction but not in corresponding propagated quantities of interest (e.g., velocity field). In this work, we investigate the prediction performance on the velocity field by propagating the corrected Reynolds stresses in PIML approach. To enrich the input features, an integrity basis of invariants is implemented. The fully developed turbulent flow in a square duct is used as the test case. The discrepancy model is trained on flow fields from several Reynolds numbers and evaluated on a duct flow at a higher Reynolds number than any of the training cases. The predicted Reynolds stresses are propagated to velocity field via RANS equations. Numerical results show excellent predictive performances in both Reynolds stresses and their propagated velocities, demonstrating the merits of the PIML approach in predictive turbulence modeling.