Bayesian Inference for Turbulence Model Uncertainty Quantification

Despite continued advances in high-fidelity turbulent flow simulations, closure models based on
the RANS equations are still widely used. However, it is common knowledge that RANS predictions are corrupted by epistemic model-form uncertainty to a degree which is unknown a-priori. Hence, to obtain a computational framework of predictive utility, a model-form Uncertainty Quantification framework is indispensable. We introduce and illustrate a methodology that can provide uncertainty estimates, without and with germane data to guide these decisions. Applying the spectral decomposition to the modeled Reynolds-Stress tensor allows for the introduction of decoupled perturbations into the baseline intensity , shape, and orientation. Within this perturbation framework, we look for a-priori known limiting physical bounds. These bounds are universal, and can be used to constrain uncertainty estimates in any predictive flow scenario. Thus, even in the absence of training data, we can maximize the spectral perturbations in order to obtain conservative uncertainty intervals. Finally, any high-fidelity reference data can be used to further constrain the uncertainty estimates using commonly available data assimilation techniques.