Towards Physics Constrained Deep Learning Based Turbulence Model Uncertainty Quantification

Turbulence Models represent the workhorse for simulations used in engineering design and analysis. Despite their low computational cost and robustness, these models suffer from substantial predictive uncertainty, most of which is epistemic. At present, the Eigenspace Perturbation Method (EPM) is the only approach to estimate these turbulence model uncertainties, using physics based perturbation to the predicted Reynolds stresses. While the EPM address the question of how to perturb the Reynolds stresses for uncertainty estimation, it does not address how much to perturb. This shortcoming leads to very generous uncertainty bounds that result in sub-optimal designs. In this investigation, we use Convolutional Neural Networks (CNN) to predict the discrepancy between predicted and actual turbulent flows. These can be utilized to modulate the degree of the perturbations in the EPM leading to a Physics Constrained Deep Learning approach for Reynolds Averaged Navier Stokes model uncertainty quantification. We test this approach on turbulent flows over aero-foils and periodic hills to show the efficacy of our approach.