Quantification and reduction of RANS model uncertainties through regional Bayesian calibration and model mixtures

Accurate turbulent closures for the Reynolds-Averaged Navier-Stokes (RANS) equations are essential for a wide range of applications in engineering. Despite a plethora of proposed RANS models, there is no consensus on a single « best » model, and model choice is based on expert judgment. The uncertainty about model choice corresponds to an « epistemic » uncertainty, i.e. due to the loss of information about turbulent motions associated with the averaging process. Furthermore, RANS model require the specification of several closure coefficients using (uncertain) data for a small set of « canonical » flows (representative of limiting behaviors of turbulence), leading to so-called « parametric » uncertainties. The quantification and reduction of both such uncertainties is then of the utmost importance for reliable flow simulations. 

Bayesian statistical methods such as Bayesian updating of model parameters and Bayesian Model Averaging (BMA) can be used to deal with both parametric and epistemic uncertainties.

In the last decades, Bayesian calibration and BMA have been applied to the quantification of RANS modelling uncertainties.

However, 1) the choice of the calibration scenarios remains a source of uncertainty and can lead to non-optimal compromise solutions for model parameters, while 2) BMA model weights are constant throughout the covariate space, in contrast with the observation that model performance depends on the local flow physics, some models being better than others at capturing some physical processes. As a consequence, BMA cannot perform better than the best model in the mixture (even if it cannot perform worse than the -unknown- worst one).

In this talk, we present and compare various approaches for calibrating "expert" models for capturing specific flow processes, and automatically combine them through a model aggregation approach that, unlike BMA, assigns regionally variable weights to the competing models. These include Clustered Bayesian averaging and mixtures of expert models. Such methods promote best-performing models in their region of expertise while downgrading unsuitable models, thus achieving better performance than any of the individual models. The procedure also provides estimates of the predictive variance. Results are shown for simple flows and turbomachinery applications.