Bayesian estimates of parameter variability in the k-e 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" turbulence closure model, for a limited class of ows. In particular we search for estimates grounded in uncertainties in the space of model closure coe- cients, for wall-bounded ows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coecients which reproduces these ows accurately, we perform 13 separate Bayesian calibrations { each at a dierent pressure gradient { using measured boundary-layer velocity proles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coecients 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 ows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer ow is made with uncertainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.