Generalized polynomial chaos for non-intrusive uncertainty quantification in computational fluid dynamics

Abstract

This chapter is concerned with the construction of polynomial surrogates of complex configurations arising in computational fluid dynamics for the purpose of propagating uncertainties pertaining to geometrical and/or operational parameters. Generalized homogeneous chaos expansions are considered and different techniques for the non-intrusive reconstruction of the polynomial expansion coefficients are outlined. A sparsity-based reconstruction approach is more particularly emphasized since it benefits from the “sparsity-of-effects” trend commonly observed on global quantities of interest such as the aerodynamic coefficients of a profile. The overall framework is illustrated on a two-dimensional transonic turbulent flow around a RAE 2822 airfoil subjected to a variable free-stream Mach number, angle of attack, and relative thickness of the profile.