A painless intrusive polynomial chaos method with RANS-based applications

Abstract

This paper presents a method for the quantification of uncertainty propagation using intrusive Polynomial Chaos Expansion (iPCE). Contrary to commonly implemented intrusive methods built on a problem specific-approach that depends on the governing PDEs, the proposed method, although intrusive in nature, can easily be implemented to any system of equations. A proper mathematical framework is developed that performs the derivation and numerical solution of the iPCE equations with little additional effort, avoiding the laborious mathematical and software development commonly associated with intrusive approaches. Computational cost, convergence and stability properties are analyzed in detail and discussed. The proposed uncertainty quantification (UQ) method is applied to the Reynolds-Averaged Navier–Stokes (RANS) equations, coupled with the Spalart–Allmaras turbulence model and results are compared with those of the non-intrusive PCE (niPCE).