Hierarchical multifidelity models for the simulation of turbulent flows*

Numerical simulations of turbulent flows are of utmost importance in physics and engineering. In practice, for a given computational budget an efficient strategy is required to address the so-called "outer-loop problem", such as flow prediction, uncertainty quantification and optimization, which typically demand multiple simulations. The present study reports our recent progress on further development and implementation of a class of hierarchical multifidelity models (MFMs) which allow for simultaneous calibration of uncertain parameters. In a Bayesian framework, at each fidelity level both model inadequacy and aleatoric uncertainties are considered. The developed MFM is applied to different flow problems as examples: i) prediction of wing polars for a standard airfoil where the angle of attack is the design parameter, and, ii) propagation of geometrical uncertainties into the quantities of interest of the turbulent flow over a periodic hill. In all problems, the predictions by the MFM are validated and the associated uncertainty is determined. The hierarchical MFM is shown to be compatible with the hierarchy of the turbulence modeling approaches and also capable of accurately handling the outer-loop problems with minimal computational cost.