  There is wide agreement that the accuracy of turbulence models suffer from
their sensitivity with respect to physical input data, the uncertainties of
user-elected parameters, as well as the model inadequacy. However, the
application of Bayesian inference to systematically quantify the uncertainties
in parameters, by means of exploring posterior probability density functions
(PPDFs), has been hindered by the prohibitively daunting computational cost
associated with the large number of model executions, in addition to daunting
computation time per one turbulence simulation. In this effort, we perform in
this paper an adaptive hierarchical sparse grid surrogate modeling approach to
Bayesian inference of large eddy simulation (LES). First, an adaptive
hierarchical sparse grid surrogate for the output of forward models is
constructed using a relatively small number of model executions. Using such
surrogate, the likelihood function can be rapidly evaluated at any point in the
parameter space without simulating the computationally expensive LES model.
This method is essentially similar to those developed in [62] for geophysical
and groundwater models, but is adjusted and applied here for a much more
challenging problem of uncertainty quantification of turbulence models. Through
a numerical demonstration of the Smagorinsky model of two-dimensional flow
around a cylinder at sub-critical Reynolds number, our approach is proven to
significantly reduce the number of costly LES executions without losing much
accuracy in the posterior probability estimation. Here, the model parameters
are calibrated against synthetic data related to the mean flow velocity and
Reynolds stresses at different locations in the flow wake. The influence of the
user-elected LES parameters on the quality of output data will be discussed.
