We demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the 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 an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D 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 an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. 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.
Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study
Manuscript received July 7, 2016; final manuscript received August 2, 2017; published online September 7, 2017. Assoc. Editor: Yan Wang. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.
Ray, J., Lefantzi, S., Arunajatesan, S., and Dechant, L. (September 7, 2017). "Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study." ASME. ASME J. Risk Uncertainty Part B. March 2018; 4(1): 011001. https://doi.org/10.1115/1.4037557
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