Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach

By Heng Xiao, Jin-Long Wu, Jian-Xun Wang, Rui Sun, Christopher J. Roy. Journal of Computational Physics, 2015

315 citations recorded by the source corpus.

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering application. For many practical flows, the turbulence models are by far the largest source of uncertainty. In this work we develop an open-box, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Simulation results suggest that, even with very sparse observations, the posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, and has potential implications in many fields in which the model uncertainty comes from unresolved physical processes. A notable example is climate modeling, where high-consequence decisions are made based on predictions (e.g., projected temperature rise) with major uncertainties originating from closure models that are used to account for unresolved or unknown physics including radiation, cloud, and boundary layer processes.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3ea634fcf17cc38f72ab89d6c2abd1c0bd99bc5d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Turbulence Modeling in the Age of Data (2018, methodology): “Xiao et al. (2016) and Wu et al. (2016) used sparse velocity ﬁeld data to infer the structure of the Reynolds stress magnitude and anisotropy.”
Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (2016, methodology): “[22] inferred the spatial distribution of the perturbations in aij and turbulent kinetic energy by assimilatingDNS data.”
Quantification of model uncertainty in RANS simulations: A review (2018, methodology): “The iterative Ensemble Kalman method has been used to infer the Reynolds stresses discrepancies by using sparse observation data of velocities [44] (see Section 4.”
Subgrid modelling for two-dimensional turbulence using neural networks (2018, background): “In accordance with the recent trends of first-principles informed learning for physics inference in turbulence (Ling & Templeton 2015; Tracey et al. 2015; Xiao et al. 2016; Singh et al. 2017; Wang et al. 2017b,a; Weatheritt & Sandberg 2017; Schaeffer 2017; Wu et al. 2018a; Raissi & Karniadakis 2018;”