Comparison of the Point-Collocation Non-Intrusive Polynomial (NIPC) and Non-Intrusive Spectral Projection (NISP) Methods for the γ-Rθ Transition Model

Thanh Hoai Nguyen,Kyoungsik Chang

doi:10.3390/app9071407

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 transitional model. Three multiple model coefficients, Ca2, Ce1, and Ce2 were considered with 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 could be found through the calculation of the Sobol index.

Highlights

Nowadays, Computational Fluid Dynamics (CFD) has become an indispensable tool in the design and development of engineering products
We considered the uncertainties of the model coefficient of the γ − Rθ transition model and applied the UncertaintyQuantification technique (UQ) technique to the parameters
In the γ − Rθ transition model, two transport equations with an extra nine model coefficients should be solved based on the SST k-ω turbulent model

Summary

Introduction

Computational Fluid Dynamics (CFD) has become an indispensable tool in the design and development of engineering products. The Polynomial Chaos (PC) approach developed by Wiener [8,9] is proposed as an alternative method. The intrusive methods require modification of the existing code into a Galerkin projection-based flow solver [10,11,12,13,14,15]. This extra work can be a big burden for CFD engineers. Whereas a non-intrusive method that enables the use of established code without any modification is considered as a promising approach in UQ and has been applied to various CFD fields by many researchers. Hosder and Walters [16,17] applied Point-Collocation Non-Intrusive Polynomial

Methods

Results

Conclusion