A tractable nonparametric probabilistic approach for modeling and quantifying model-form uncertainty in turbulent CFD

This paper presents an innovative, computationally tractable approach for modeling and quantifying model-form uncertainty (MFU) in viscous computational fluid dynamics (CFD) models. It distinguishes between two sources of uncertainty: those related to turbulence modeling and other sources such as wall and far-field boundary conditions. The proposed approach comprises two complementary and coupled methods for uncertainty quantification (UQ): one targeting uncertainties in Reynolds stress modeling; and the other addressing all remaining model-form and parametric uncertainties. The first method decomposes the Reynolds stress tensor into a trace-vanishing deviatoric component and a spherical part. It then constructs a hyperparameterized probability model for the eigenvalues of the deviatoric component, based on its spectral algebraic properties. Further probabilistic modeling yields a complete hyperparameterized model for the Reynolds stress tensor, with each realization corresponding to an admissible turbulence model within a specific family. The second method adapts a recently developed nonparametric probabilistic approach for modeling and quantifying MFU to the context of this study. It relies on a probabilistic, projection-based model order reduction (PMOR) technique that is also hyperparameterized, ensuring computational tractability for UQ. The hyperparameters for both methods are simultaneously determined by formulating and minimizing an appropriate data-driven probabilistic loss function. Additionally, the methodology accounts for the uncertainties associated with PMOR, which is introduced to achieve efficient Monte Carlo simulations. The efficacy of the overall approach proposed for UQ in large-scale CFD computations is demonstrated through the Reynolds-averaged Navier-Stokes-based aerodynamic analysis of a rigid NASA Common Research Model configuration in the transonic flow regime, for which wind tunnel data is available.