Bayesian Predictions of Reynolds-Averaged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates

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, 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 to obtain a stochastic estimate of a Quantity-of-Interest in an unmeasured prediction scenario by i) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and ii) by computing a weighted posterior predictive distribution. While step ii) has a negligible computational cost, step i) requires a large number of samples of the solver.

Conditioning and accurate solutions of Reynolds average Navier–Stokes equations with data-driven turbulence closures

“…The use of perturbations of the eigenvalues of the Reynolds stress tensor (Emory, Larsson & Iaccarino 2013;Gorlé & Iaccarino 2013;Margheri et al 2014), as well as the eigenvectors (Iaccarino, Mishra & Ghili 2017;Thompson et al 2019) were employed systematically. Data-driven approaches using Bayesian estimates are also an important adopted strategy (Edeling, Cinnella & Dwight 2014a;Edeling et al 2014bEdeling et al , 2018Xiao et al 2016). The interested reader is referred to a recent review by Xiao & Cinnella (2019) and the references therein.…”

“…Data-driven approaches using Bayesian estimates are also an important adopted strategy (Edeling, Cinnella & Dwight 2014 a ; Edeling et al. 2014 b , 2018; Wu, Wang & Xiao 2016; Xiao et al. 2016).…”

Surrogate-Assisted Parametric Study of a Wing Fences for Unmanned Aerial Vehicles

“…However, confronted with the staggering computational cost of a single evaluation, an efficient methodology is sought to explore the design space based on a number of samples. An established methodology to answer the problem at hand is found in the field of surrogate modeling, which is actively used for aerospace applications: calibration of turbulence models [21], modeling of flight data [22,23], uncertainty quantification [24][25][26] and robust [27,28], multi-objective [5], shape [29] and multi-disciplinary [30] optimization. This implies that, after defining the objective function and the design space, a design of experiments (DoE) is set up to select samples in the design space, for which the objective function is subsequently calculated and of which a surrogate is defined.…”

“…25 if three meshes have been used to establish the .Y = (x) = (x 1 , ..., x ) = (x , x )+ =1 = +1 = +1, , (x , x , x ) + ... + 1,..., (x 1 , ..., x )…”

Robust prediction of dense gas flows under uncertain thermodynamic models

“…This is however not the case in general, so that a key point is to find a suitable a priori criterion for choosing the scenario weights. An empirical criterion, based on the level of agreement among the competing models calibrated on the same scenario, was proposed in [28] and successfully applied to the prediction of a variety of turbulent perfect gas flows in [28,29].…”