A Random Matrix Approach for Quantifying Model-Form Uncertainties in Turbulence Modeling

Abstract

With the ever-increasing use of Reynolds-Averaged Navier--Stokes (RANS) simulations in mission-critical applications, the quantification of model-form uncertainty in RANS models has attracted attention in the turbulence modeling community. Recently, a physics-based, nonparametric approach for quantifying model-form uncertainty in RANS simulations has been proposed, where Reynolds stresses are projected to physically meaningful dimensions and perturbations are introduced only in the physically realizable limits. However, a challenge associated with this approach is to assess the amount of information introduced in the prior distribution and to avoid imposing unwarranted constraints. In this work we propose a random matrix approach for quantifying model-form uncertainties in RANS simulations with the realizability of the Reynolds stress guaranteed. Furthermore, the maximum entropy principle is used to identify the probability distribution that satisfies the constraints from available information but without introducing artificial constraints. We demonstrate that the proposed approach is able to ensure the realizability of the Reynolds stress, albeit in a different manner from the physics-based approach. Monte Carlo sampling of the obtained probability distribution is achieved by using polynomial chaos expansion to map independent Gaussian random fields to the Reynolds stress random field with the marginal distributions and correlation structures as specified. Numerical simulations on a typical flow with separation have shown physically reasonable results, which verifies the proposed approach. Therefore, the proposed method is a promising alternative to the physics-based approach for model-form uncertainty quantification of RANS simulations. The method explored in this work is general and can be extended to other complex physical systems in applied mechanics and engineering.

42 pages, 10 figures

References in corpus (4)

• Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach
• A Bayesian Calibration-Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations
• Quantification of Uncertainties in Turbulence Modeling: A Comparison of Physics-Based and Random Matrix Theoretic Approaches
• Incorporating Prior Knowledge for Quantifying and Reducing Model-Form Uncertainty in RANS Simulations

Cited by in corpus (18)

• Turbulence Modeling in the Age of Data
• Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach
• Data-Driven Modelling of the Reynolds Stress Tensor using Random Forests with Invariance
• Feature selection and processing of turbulence modeling based on an artificial neural network
• Enhancing the SST Turbulence Model with Symbolic Regression: A Generalizable and Interpretable Data-Driven Approach
• Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models
• Quantification of Uncertainties in Turbulence Modeling: A Comparison of Physics-Based and Random Matrix Theoretic Approaches
• A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term
• Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests
• Variational assimilation of sparse time-averaged data for efficient adjoint-based optimization of unsteady RANS simulations
• RANS predictions for high-speed flows using enveloping models
• Quantification of Reynolds-averaged-Navier-Stokes model form uncertainty in transitional boundary layer and airfoil flows
• Spectral adjoint-based assimilation of sparse data in unsteady simulations of turbulent flows
• An uncertainty estimation module for turbulence model predictions in SU2
• Quantification of Model Uncertainty in RANS Simulations: A Review
• Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification
• Graph Laplacian-based Bayesian Multi-fidelity Modeling
• Numerical Solution of Free Stochastic Differential Equations