Data-driven Eigenspace Perturbations for RANS Uncertainty Quantification*

Turbulence models are indispensable yet limited in their accuracy and therefore a significant source of model-form uncertainty in turbulent flow simulations. Data-free perturbations to the spectral decomposition of the Reynolds stress tensor can be used to obtain uncertainty envelopes for quantities of interest. Such data-free perturbations perturb at spatially uniform strength regardless of the expected local inaccuracy of the turbulence model. Since turbulence models work better in some situations than in others, this uniform approach tends to lead to an overestimation of the model-form uncertainty.

Non-uniform data-driven perturbations are able to account for a spatially varying degree of inaccuracy in the turbulence model predictions. A machine learning model trained on test cases using RANS and high-fidelity data is used to predict a local perturbation strength based on mean flow features. 

These data-driven perturbations are shown to give envelopes that are more characteristic of the true uncertainty in the predictions. Besides, a data-driven best estimate is presented to complement the uncertainty envelopes.

Generalization of this approach is studied over several training and test cases.