Flow, Turbulence and Combustion

, Volume 100, Issue 3, pp 593–616 | Cite as

Data-Free and Data-Driven RANS Predictions with Quantified Uncertainty

  • W. N. EdelingEmail author
  • G. Iaccarino
  • P. Cinnella


For the purpose of estimating the epistemic model-form uncertainty in Reynolds-Averaged Navier-Stokes closures, we propose two transport equations to locally perturb the Reynolds stress tensor of a given baseline eddy-viscosity model. The spatial structure of the perturbations is determined by the proposed transport equations, and thus does not have to be inferred from full-field reference data. Depending on a small number of model parameters and the local flow conditions, a ’return to eddy viscosity’ is described, and the underlying baseline state can be recovered. In order to make predictions with quantified uncertainty, we identify two separate methods, i.e. a data-free and data-driven approach. In the former no reference data is required and computationally inexpensive intervals are computed. When reference data is available, Bayesian inference can be applied to obtained informed distributions of the model parameters and simulation output.


RANS modeling Uncertainty quantification Bayesian inference Return to eddy viscosity Lag model 


Compliance with Ethical Standards

This investigation was funded by the United States Department of Energy’s (DoE) National Nuclear Security Administration (NNSA) under the Predictive Science Academic Alliance Program II (PSAAP II) at Stanford University.

Conflict of interests

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Center for Turbulence ResearchStanford UniversityStanfordUSA
  2. 2.Laboratoire DynFluidArts et Métiers ParisTechParisFrance

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