BAYESIAN INFERENCE OF γ-Reθ TRANSITIONAL MODEL COEFFICIENT BASED ON PC-NIPC METHOD

Abstract

In the present work, a comparative study of two major Non-Intrusive Polynomial Chaos methods, Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) and Non-Intrusive Spectral Projection (NISP), was conducted for the transitional γ-Reθ transitional model. Three multiple model coefficients, ca2, ce1, and ce2, were considered as multiple random inputs with the assumption of uniform distributions with 10% deviation. The target transitional flows were one around a flat plate and Aerospatiale A-airfoil. Deterministic solutions were obtained by employing the open source software OpenFOAM. The results of two methods were compared to the results of Monte Carlo simulation with 500 runs. The order convergence of the mean value and the standard deviation (STD) were compared in terms of the quantities of interest, drag and lift coefficients. Further, the most effective model coefficient for each transitional flow can be found through the calculation of the Sobol index. And then we apply Bayesian Inference to demonstrate inverse problem to find the mean and stand deviation of the parameters constant in γ-Reθ transitional model, and create the correlation matrix among the parameters with surrogate model which was made by Point-Collocation Non-intrusive Polynomial Chaos. The Bayesian parameter calibration approach based on gPCE is integrated to the developed comprehensive framework of analyzing and identification. The gPCE is applied to the parameter calibration in two ways. The first one is using the gPC approximation as the surrogate model. The second fashion is expanding the recursive Bayesian estimator with the polynomial chaos basis. This technique, which is quite new, provides good results and has attractive properties.