Quantification of Uncertainty in Aeroacoustic Cavity Noise Simulations with a Discontinuous Galerkin Solver

The underlying physical mechanisms of aeroacoustic cavity feedback originate from a highly non-linear and multiscale interaction between the turbulent hydrodynamics and acoustics. This multiscale nature causes a strong sensitivity of the noise generation process with respect to small perturbations of the incoming flow. In consequence, small uncertainties of input parameters or boundary conditions may have a large influence on the resulting acoustic signal which may lead to unreliable numerical predictions and to discrepancies between experimental and numerical results.
The research area of uncertainty quantification provides different mathematical tools to quantify the effect of such uncertain input parameters on the numerical solution and derived quantities which requires a particularly efficient deterministic flow solver. Thus, to meet the necessary efficiency requirements, the first part of this thesis extends an existing discontinuous Galerkin spectral element flow solver by a zonal large-eddy simulation (LES) framework.
With an efficient LES framework at hand, the second part of this work is dedicated to the implementation and validation of an uncertainty quantification framework to analyze the influence of uncertain input and boundary conditions on the resulting acoustic signal. This framework consists of two polynomial-based methods, the stochastic Galerkin method and the non-intrusive spectral projection method, and two random sampling-based methods, the Monte Carlo and the multilevel Monte Carlo method. Out of these, the non-intrusive spectral projection method in combination with the zonal LES framework is finally used to conduct turbulent aeroacoustic cavity simulations with uncertain boundary conditions in order to investigate stochastic moments of the resulting aeroacoustic signal.