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Turbulence modeling is a critical component in numerical simulations ofindustrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations.However, after decades of efforts in the turbulence modeling community,universally applicable RANS models with predictive capabilities are stilllacking. Recently, data-driven methods have been proposed as a promisingalternative to the traditional approaches of turbulence model development. Inthis work we propose a data-driven, physics-informed machine learning approachfor predicting discrepancies in RANS modeled Reynolds stresses. Thediscrepancies are formulated as functions of the mean flow features. By using amodern machine learning technique based on random forests, the discrepancyfunctions are first trained with benchmark flow data and then used to predictReynolds stresses discrepancies in new flows. The method is used to predict theReynolds stresses in the flow over periodic hills by using two training flowscenarios of increasing difficulties: (1) the flow in the same periodic hillsgeometry yet at a lower Reynolds number, and (2) the flow in a different hillgeometry with a similar recirculation zone. Excellent predictive performanceswere observed in both scenarios, demonstrating the merits of the proposedmethod. Improvement of RANS modeled Reynolds stresses enabled by the proposedmethod is an important step towards predictive turbulence modeling, where theultimate goal is to predict the quantities of interest (e.g., velocity field,drag, lift) more accurately by solving RANS equations with the Reynoldsstresses obtained therefrom.

A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data