Efficient prediction of turbulent flow quantities using a Bayesian hierarchical multifidelity model

Abstract

Multifidelity models (MFMs) can be used to construct predictive models for flow quantities of interest (QoIs) over the space of uncertain/design parameters, with the purpose of uncertainty quantification, data fusion and optimization. For numerical simulation of turbulence, there is a hierarchy of methodologies ranked by accuracy and cost, where each methodology may have several numerical/modelling parameters that control the predictive accuracy and robustness of its resulting outputs. Compatible with these specifications, the present hierarchical MFM strategy allows for simultaneous calibration of the fidelity-specific parameters in a Bayesian framework as developed by Gohet al.(Technometrics, vol. 55, no. 4, 2013, pp. 501–512). The purpose of the MFM is to provide an improved prediction, mainly interpolation over the range covered by training data, by combining lower- and higher-fidelity data in an optimal way for any number of fidelity levels; even providing confidence intervals for the resulting QoI. The capabilities of the MFM are first demonstrated on an illustrative toy problem, and it is then applied to three realistic cases relevant to engineering turbulent flows. The latter include the prediction of friction at different Reynolds numbers in turbulent channel flow, the prediction of aerodynamic coefficients for a range of angles of attack of a standard airfoil and the uncertainty propagation and sensitivity analysis of the separation bubble in the turbulent flow over periodic hills subject to geometrical uncertainties. In all cases, based on only a few high-fidelity data samples, the MFM leads to accurate predictions of the QoIs. The result of the uncertainty quantification and sensitivity analyses are also found to be accurate compared with the ground truth in each case.