Computational methods for analyzing aircraft noise above ground with general topography and impedance

The need to analyze aircraft noise over ground with general properties occurs in various applications, most notably in environmental engineering, where the analysis of the sound pressure level (SPL) distribution near the ground due to aircraft noise is desired. Since the human hearing range is very wide, the determination of the SPL distribution for a given source spectrum is not trivial and may be regarded as a multiscale problem. One has to solve repeatedly, for many different wave numbers, the Helmholtz equation in the upper half space while imposing the given impedance boundary condition on the possibly non-flat ground. An efficient Helmholtz solver must therefore be incorporated in the scheme that finds the SPL distribution. Three totally different computational methods that may be used to solve this problem are considered here: A fictitious sources method, a parabolic approximation method and a wave-enriched finite element method (with two versions: PUM and GFEM). The three methods are compared in terms of their computational properties, and numerical examples are presented to demonstrate their performance.