The acoustic transmissions and reflections of plane waves at duct singularities can be represented with so-called scattering matrices. This paper shows how to extract scattering matrices utilizing linearized compressible flow equations and provides a comparative study of different governing equations, namely the Helmholtz, linearized Euler and linearized Navier–Stokes equations. A discontinuous Galerkin finite element method together with a two-source forcing is employed. With this method, the scattering matrix for a radial swirler of a combustion test-rig is computed and validated against the results of a fully compressible Large-Eddy-Simulation. Analogously, the scattering behavior of an axial swirler is investigated. The influence of acoustic-hydrodynamic interactions, viscous effects as well as unsteady boundary layers on the results is investigated for both configurations. A thermoacoustic stability analysis of the combustion test-rig housing the axial swirler is carried out, utilizing the scattering matrix of the swirler. Major influence of the reflections coming from the swirler on the thermoacoustic eigenfrequencies is found.