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Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS)models are still the workhorse tools for turbulent flow simulations in today'sengineering application. For many practical flows, the turbulence models are byfar the largest source of uncertainty. In this work we develop an open-box,physics-informed Bayesian framework for quantifying model-form uncertainties inRANS simulations. Uncertainties are introduced directly to the Reynoldsstresses and are represented with compact parameterization accounting forempirical prior knowledge and physical constraints (e.g., realizability,smoothness, and symmetry). An iterative ensemble Kalman method is used toassimilate the prior knowledge and observation data in a Bayesian framework,and to propagate them to posterior distributions of velocities and otherQuantities of Interest (QoIs). We use two representative cases, the flow overperiodic hills and the flow in a square duct, to evaluate the performance ofthe proposed framework. Simulation results suggest that, even with very sparseobservations, the posterior mean velocities and other QoIs have significantlybetter agreement with the benchmark data compared to the baseline results. Atmost locations the posterior distribution adequately captures the true modelerror within the developed model form uncertainty bounds. The framework is amajor improvement over existing black-box, physics-neutral methods formodel-form uncertainty quantification, where prior knowledge and details of themodels are not exploited. This approach has potential implications in manyfields in which the governing equations are well understood but the modeluncertainty comes from unresolved physical processes.

Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach