  Proper quantification and propagation of uncertainties in computational
simulations are of critical importance. This issue is especially challenging
for CFD applications. A particular obstacle for uncertainty quantifications in
CFD problems is the large model discrepancies associated with the CFD models
used for uncertainty propagation. Neglecting or improperly representing the
model discrepancies leads to inaccurate and distorted uncertainty distribution
for the Quantities of Interest. High-fidelity models, being accurate yet
expensive, can accommodate only a small ensemble of simulations and thus lead
to large interpolation errors and/or sampling errors; low-fidelity models can
propagate a large ensemble, but can introduce large modeling errors. In this
work, we propose a multi-model strategy to account for the influences of model
discrepancies in uncertainty propagation and to reduce their impact on the
predictions. Specifically, we take advantage of CFD models of multiple
fidelities to estimate the model discrepancies associated with the
lower-fidelity model in the parameter space. A Gaussian process is adopted to
construct the model discrepancy function, and a Bayesian approach is used to
infer the discrepancies and corresponding uncertainties in the regions of the
parameter space where the high-fidelity simulations are not performed. The
proposed multi-model strategy combines information from models with different
fidelities and computational costs, and is of particular relevance for CFD
applications, where a hierarchy of models with a wide range of complexities
exists. Several examples of relevance to CFD applications are performed to
demonstrate the merits of the proposed strategy. Simulation results suggest
that, by combining low- and high-fidelity models, the proposed approach
produces better results than what either model can achieve individually.
