Hierarchical Bayesian multifidelity modelling applied to turbulent flows

Conducting high-fidelity studies in fluid mechanics can be prohibitively expensive, particularly at high Reynolds numbers. Thus, it is necessary to develop accurate yet cost-effective models for outer-loop problems involving turbulent flows. One way is multifidelity models (MFMs) which aim at accurately predicting quantities of interest (QoIs) and their stochastic moments by combining the data obtained from different fidelities. 

When constructing MFMs, a balance is sought between a few expensive (but accurate) simulations and many more inexpensive (but potentially less accurate) simulations. Two main characteristics have to be considered. 1) there is a distinguishable hierarchy in the fidelity of approaches such as Reynolds-averaged Navier-Stokes simulation (RANS), hybrid RANS-LES, wall-modeled and wall-resolved LES, and DNS. 2) the outcome of any of these approaches can be potentially uncertain due to various inherent uncertainties.

In our multifidelity modeling approach, the calibration parameters as well as the hyperparameters appearing in the Gaussian processes are simultaneously estimated within a Bayesian framework. GP provides a natural way for incorporating observational uncertainty in the data. The Bayesian inference is done using a Markov Chain Monte Carlo (MCMC) approach.

The efficiency of the HC-MFM is evaluated for various problems involving turbulent flows. We first predict the lift coefficient of a wing at Reynolds number 1.6M. The flow angle of attack (AoA) is the design parameter and the data fed into the MFM comprises of: wind-tunnel experiments, detached-eddy simulations (DES) and 2D RANS. Turbulence intensity and the stall AoA is considered as a calibration parameter. We will also study the periodic hill case to assess the effect of geometry, and provide comparison to more classical co-Krigin approaches.