Comparison Between Linear and Hierarchical Multifidelity Models for Uncertainty Quantification in Turbulent Flows

Multifildelity models (MFMs) have received considerable attention in recent years for making outer-loop problems in computational fluid dynamics (CFD) more affordable. A recent study by Rezaeiravesh et al. [9] showed that a hierarchical MFM within a Bayesian framework can be an appropriate choice for applications with turbulent flows. In the present study, this model is compared to a linear co-kriging MFM that has been widely used in literature. The uncertainty quantification in a turbulent flow over periodic hills is considered, where two parameters affecting the geometry of the hills are assumed to be uncertain. Both MFMs are found to be capable of accurately estimating the stochastic moments and the Sobol sensitivity indices of the quantity of interest (QoI). However, for the probability distribution of the QoI, the hierarchical model showed a better performance. Future detailed examinations will reveal the conditions under which any of these MFM strategies can be used with high reliability in the results.