Towards multifidelity models with calibration for turbulent flows

High-fidelity scale-resolving simulations of turbulent flows can be prohibitively expensive, especially at high Reynolds numbers. Therefore, multifidelity models (MFM) can be highly relevant for constructing predictive models for flow quantities of interest (QoIs), uncertainty quantification, and optimization. For numerical simulation of turbulence, there is a hierarchy of methodologies. On the other hand, there are calibration parameters in each of these methods which control the predictive accuracy of the resulting outputs. Compatible with these, the hierarchical MFM strategy which allows for simultaneous calibration of the model parameters as developed by Goh et al. [7] within a Bayesian framework is considered in the present study. The multifidelity model is applied to two cases related to wall-bounded turbulent flows. The examples are the prediction of friction at different Reynolds numbers in turbulent channel flow, and the prediction of aerodynamic coefficients for a range of angles of attack of a standard airfoil. In both cases, based on a few high-fidelity datasets, the MFM leads to accurate predictions of the QoIs as well as an estimation of uncertainty in the predictions.