Sparse grids-based stochastic approximations with applications to aerodynamics sensitivity analysis

This work compares sample-based polynomial surrogates, well suited for moderately high-dimensional stochastic problems. In particular, generalized polynomial chaos in its sparse pseudospectral form and stochastic collocation methods based on both isotropic and dimension-adapted sparse grids are considered. Both classes of approximations are compared, and an improved version of a stochastic collocation with dimension adaptivity driven by global sensitivity analysis is proposed. The stochastic approximations efficiency is assessed on multivariate test function and airfoil aerodynamics simulations. The latter study addresses the probabilistic characterization of global aerodynamic coefficients derived from viscous subsonic steady flow about a NACA0015 airfoil in the presence of geometrical and operational uncertainties with both simplified aerodynamics model and Reynolds-Averaged Navier-Stokes (RANS) simulation. Sparse pseudospectral and collocation approximations exhibit similar level of performance for isotropic sparse simulation ensembles. Computational savings and accuracy gain of the proposed adaptive stochastic collocation driven by Sobol' indices are patent but remain problem-dependent.