Estimation of Model Error Using Bayesian Model-Scenario Averaging with <Emphasis Type="Italic">Maximum a Posterori</Emphasis>-Estimates

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Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates

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

Abstract The lack of an universal modelling approach for turbulence in Reynolds-Averaged Navier–Stokes simulations creates the need for quantifying the modelling error without additional validation data. Bayesian Model-Scenario Averaging (BMSA), which exploits the variability on model closure coefficients across several flow scenarios and multiple models, gives a stochastic, a posteriori estimate of a quantity of interest. The full BMSA requires the propagation of the posterior probability distribution of the closure coefficients through a CFD code, which makes the approach infeasible for industrial relevant flow cases. By using maximum a posteriori (MAP) estimates on the posterior distribution, we drastically reduce the computational costs. The approach is applied to turbulent flow in a pipe at $R e =$ 44,000 over 2D periodic hills at $R e_{H} = 5600$ , and finally over a generic falcon jet test case (Industrial challenge IC-03 of the UMRIDA project).