Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

We demonstrate a statistical procedure for learning a highorder 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