Bayesian uncertainty quantification applied to RANS turbulence models

By Todd A. Oliver, Robert D. Moser. 2011

156 citations recorded by the source corpus.

A Bayesian uncertainty quantification approach is developed and applied to RANS turbulence models of fully-developed channel flow. The approach aims to capture uncertainty due to both uncertain parameters and model inadequacy. Parameter uncertainty is represented by treating the parameters of the turbulence model as random variables. To capture model uncertainty, four stochastic extensions of four eddy viscosity turbulence models are developed. The sixteen coupled models are calibrated using DNS data according to Bayes' theorem, producing posterior probability density functions. In addition, the competing models are compared in terms of two items: posterior plausibility and predictions of a quantity of interest. The posterior plausibility indicates which model is preferred by the data according to Bayes' theorem, while the predictions allow assessment of how strongly the model differences impact the quantity of interest. Results for the channel flow case show that both the stochastic model and the turbulence model affect the predicted quantity of interest. The posterior plausibility favors an inhomogeneous stochastic model coupled with the Chien k-ϵ model. After calibration with data at Reτ = 944 and Reτ = 2003, this model gives a prediction of the centerline velocity at Reτ = 5000 with uncertainty of approximately ± 4%.

Subfields: Aerospace Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/92c3d7eecbc199b1498ed9ec179441aee3aa273b

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Citations in the corpus

Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (2016, methodology): “[13, 14] employ Bayesian model averaging[15] to calibrate model coefficients.”
Aerodynamic shape optimization for minimum robust drag and lift reliability constraint (2016, methodology): “For other parameters, such as the turbulence model parameters, the uncertainties can be quantified by experimental measurements using for instance Bayesian techniques [40,2,33,7,12].”
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks (2018, methodology): “Earlier work in quantifying the uncertainty and calibration of turbulence models focused on treating model parameters as random variables and sampling via Monte Carlo to obtain a predictive distribution of outcomes [10, 11].”
Quantification of model uncertainty in RANS simulations: A review (2018, methodology): “Different statistical models can be obtained for different choices of the covariance matrix, and more complex choices for the inadequacy term have also been investigated [110].”