Bayesian estimates of parameter variability in the k-ε turbulence model

In this paper we are concerned with obtaining estimates for the error in Reynolds-averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k-epsilon turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coefficients, for wall-bounded flows at a variety of favorable and adverse pressure gradients. In order to estimate the spread of closure coefficients which reproduces these flows accurately, we perform 13 separate Bayesian calibrations - each at a different pressure gradient - using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model-inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the total solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncertainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data. (C) 2013 Elsevier Inc. All rights reserved.