Bayesian predictions of reynolds-averaged navier–stokes uncertainties using maximum a posteriori estimates

Wouter N. Edeling, Martin Schmelzer, Richard P. Dwight, Paola Cinnella

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

Computational fluid dynamics analyses of high-Reynolds-number flows mostly rely on the Reynolds-averaged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, which are calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian model-scenario averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows a stochastic estimate of a quantity of interest in an unmeasured prediction scenario to be obtain by 1) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and 2) computing a weighted posterior predictive distribution. Although step 2 has a negligible computational cost, step 1 requires a large number of samples of the solver. To enable the application of the proposed approach to computationally expensive flow configurations, a modified formulation is used where a maximum posterior probability approximation is used to drastically reduce the computational burden. The predictive capability of the proposed simplified approach is assessed for two-dimensional separated and three-dimensional compressible flows.

Original languageEnglish
Pages (from-to)2018-2029
Number of pages12
JournalAIAA Journal
Volume56
Issue number5
DOIs
Publication statusPublished - 1 Jan 2018

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