Adaptive Model Refinement Approach for Bayesian Uncertainty Quantification in Turbulence Model

Abstract: The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference in a high-dimensional design space, which limits uncertainty quantification for complex flow configurations. Borrowing ideas from stratified sampling and inherited sampling, an adaptive model refinement approach is proposed in this work, which concentrates on asymptotically improving the local accuracy of the surrogate model in the high-posterior-density region by adaptively appending model evaluation points. To achieve this goal, a modification of inherited Latin hypercube sampling is proposed and then integrated into the Bayesian framework. The effectiveness and efficiency of the proposed approach are demonstrated through a two-dimensional heat source inversion problem and its extension to a high-dimensional design space. Compared with the prior-based method, the adaptive model refinement approach has the ability to obtain more reliable inference results using fewer evaluation points. Finally, the approach is applied to parametric uncertainty quantification of the Menter shear-stress transport turbulence model for an axisymmetric transonic bump flow and provides convincing numerical results.