Application of supervised learning to quantify uncertainties in turbulence and combustion modeling

The accuracy of low-fidelity models of turbulent flow such as those based on the Reynolds Averaged Navier–Stokes (RANS) equations can be questionable, especially when these models are applied in situations different from those in which the models were calibrated. At present, there is no general method to quantify structural uncertainties in such models. Greater accuracy and a reliable quantification of modeling errors is much needed to expand the use of affordable simulation models in engineering design and analysis. In this paper, we introduce a methodology aimed at improving low-fidelity models of turbulence and combustion and obtaining error bounds. Towards this end, we first develop a new machine learning algorithm to construct a stochastic model of the error of low-fidelity models using information from higher-fidelity data sets. Then, by applying this error model to the lowfidelity result, we obtain better approximations of uncertain model outputs and generate confidence intervals on the prediction of simulation outputs. We apply this technique to two representative flow problems. The first application is in flamelet-based simulations to model combustion in a turbulent mixing layer; and the second application is in the prediction of the anisotropy of turbulence in a non-equilibrium boundary layer flow. We demonstrate that our methodology can be used to improve aspects of predictive modeling while offering a route towards obtaining error bounds.