Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics

Alexander Litvinenko, TU Braunschweig

Abstract: The problem to be considered is the system of Navier-Stokes equations with k-ω turbulence model, the computational domain is RAE- 2822 airfoil. We research how uncertainties in the input data and in the computational domain propagate in the uncertainties in the solution. The solution of this problem (pressure, density, velosity etc) is represented 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 works on the fly, is based on QR-decomposition and has a linear complexity. This low-rank approximation allows us an effective postprocessing (com- putation of the mean value, variance, exceedance probability) with drastically reduced memory requirements.