Our goal is to make predictive simulations with Reynolds-Averaged Navier-Stokes (RANS) turbulence models, i.e. simulations with a systematic treatment of model and data uncertainties and their propagation through a computational model to produce predictions of quantities of interest with quantified uncertainty . To do so, we make use of the robust Bayesian statistical framework, in which the uncertainty is represented by probability.
We search for estimates of the uncertainties in the space of model coefficients, for a large range of different calibration scenarios. To capture the coefficient variability over the calibrations scenarios we perform multiple Bayesian calibrations, resulting in a set of joint posterior probability distributions. For an unmeasured prediction scenario, we then combine these distributions into a single predictive quantity of interest using Bayesian Model-Scenario Averaging (BMSA). This framework combines multiple turbulence models and calibration scenarios, allowing one to make predictions with quantified uncertainty.
A full BMSA approach would require many samples from the RANS code, making it computationally expensive for many flow cases of interest. To apply BMSA to complex topologies, we investigated two options. First, one can replace the expensive RANS code with a cheaper surrogate model, e.g. the Simplex-Stochastic Collocation Method . Alternatively, we can keep the full RANS model and instead replace the expensive posterior distributions with Dirac delta distributions centered at their Maximum A-Posteriori values.
 T. Oden, R. Moser, and O. Ghattas. Computer predictions with quantified uncertainty. Technical report, ICES-REPORT 10-39, The institute for Computational Engineering and Sciences, The University of Texas at Austin, 2010.
 J.A.S. Witteveen and G. Iaccarino. Simplex Stochastic Collocation with ENO-type stencil selection for robust uncertainty quantification. Journal of Computational Physics, 239:1–21, 2013.