  Turbulence modeling is a critical component in numerical simulations of
industrial 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 still
lacking. Recently, data-driven methods have been proposed as a promising
alternative to the traditional approaches of turbulence model development. In
this work we propose a data-driven, physics-informed machine learning approach
for predicting discrepancies in RANS modeled Reynolds stresses. The
discrepancies are formulated as functions of the mean flow features. By using a
modern machine learning technique based on random forests, the discrepancy
functions are first trained with benchmark flow data and then used to predict
Reynolds stresses discrepancies in new flows. The method is used to predict the
Reynolds stresses in the flow over periodic hills by using two training flow
scenarios of increasing difficulties: (1) the flow in the same periodic hills
geometry yet at a lower Reynolds number, and (2) the flow in a different hill
geometry with a similar recirculation zone. Excellent predictive performances
were observed in both scenarios, demonstrating the merits of the proposed
method. Improvement of RANS modeled Reynolds stresses enabled by the proposed
method is an important step towards predictive turbulence modeling, where the
ultimate goal is to predict the quantities of interest (e.g., velocity field,
drag, lift) more accurately by solving RANS equations with the Reynolds
stresses obtained therefrom.
