Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework

Turbulence modeling introduces large model-form uncertainties in the predictions. Recently, data-driven methods have been proposed as a promising alternative by using existing databases of experiments or high-fidelity simulations. In this talk, we present a comprehensive framework for augmenting turbulence models with physics-informed machine learning, illustrating a complete workflow from identification of input features to final prediction of mean velocities. The learned model satisfies two key requirements in turbulence modeling: Galilean invariance and coordinate rotational invariance. This framework consists of three components: (1) reconstructing Reynolds stress modeling discrepancies based on DNS data via machine learning techniques, (2) assessing the prediction confidence a priori based on distance metrics in the mean flow features space, and (3) propagating the predicted Reynolds stress field to mean velocity field by using physics-informed stabilization. Several flows with massive separations are investigated to evaluate the performance of the proposed framework. Significant improvements over the baseline RANS simulation are observed for the Reynolds stress and the mean velocity fields.