An efficient approach for quantifying parameter uncertainty in the SST turbulence model

Abstract In this work, an efficient approach for quantifying the parameter uncertainty for expensive computer models is proposed, which combines the high dimensional model representation (HDMR) technique and the Gaussian process machine learning (GPML) method to construct the surrogate model, then the so-constructed surrogate is used in the Bayesian inference procedure to obtain the posterior distribution of the model parameters. The applications of the proposed approach to simple mathematical functions are investigated, demonstrating its efficiency and accuracy for both continuous function and function with discontinuities. The computer design of the sampling points based on GPML is also proposed and the results show that the proposed method is promising in terms of both efficiency and extensibility to high dimensional problems. After testing the proposed approach with simple mathematical functions, it is applied to the two equation SST turbulence model for hypersonic flow over flat plate with a wide range of Mach numbers. A Bayesian scenario-averaging method based on the flow quantities that can characterize both the flow scenario and the model’s performance in the scenario is proposed and it is employed for the model predictions of new flow scenarios. The results show that the prediction mean values match well with the DNS data and the corresponding uncertainties are well captured.

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