Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics
The problem to be considered is the stationar system of Navier-Stokes equations with uncertain parameters and uncertain computational domain. We research how uncertainties in the angle of attack, in the Mach number and in the geometry of the airfoil propagate in the solution. The uncertain solution of this problem (pressure, density, velocity etc) is approximated via random fields. Since the whole set of realisations of these random fields are too much information, we demonstrate an algorithm of their low-rank approximation. This algorithm, working on the fly, is based on the QR-decomposition and has a linear complexity. This low-rank approximation allows us an effective postprocessing (computation of the mean value, variance, exceedance probability) with drastically reduced memory requirements.