Learning an eddy viscosity model using shrinkage and Bayesian calibration: A jet-in-crossflow case study

[+] Author and Article Information
Jaideep Ray

MS 9159, PO Box 969, Sandia National Laboratories, Livermore, California 94550

Sophia Lefantzi

MS 9152, PO Box 969, Sandia National Laboratories, Livermore, California 94550

Srinivasan Arunajatesan

MS 0825, PO Box 5800, Sandia National Laboratories, Albuquerque, New Mexico 87185

Lawrence DeChant

MS 0825, PO Box 5800, Sandia National Laboratories, Albuquerque, New Mexico 87185

1Corresponding author.

ASME doi:10.1115/1.4037557 History: Received July 07, 2016; Revised August 02, 2017


We demonstrate a statistical procedure for learning a high-order eddy viscosity model from experimental data and using it to improve the predictive skill of a Reynolds-Averaged Navier Stokes simulator. The method is tested in a 3D, transonic jet-in-crossflow configuration. The process starts with a cubic eddy viscosity model developed for incompressible flows. It is fitted to limited experimental jet-in-crossflow data using shrinkage regression. The shrinkage process removes all terms from the model, except an intercept, a linear term and a quadratic one involving the square of the vorticity. The shrunk eddy viscosity model is implemented in a Reynolds Averaged Navier-Stokes simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo method. A three-dimensional probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside a Markov chain Monte Carlo loop is mitigated by using surrogate models ("curve-fits"). A support vector machine classifier is used to impose our prior belief regarding parameter values, specifically to exclude non-physical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and cubic eddy viscosity models. We find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.

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