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**Example text**

We understand CAA here in the broadest possible sense – that is, as a process using some kind of numerical computation to produce acoustical information for aerodynamic phenomena. That obviously includes all flavors of acoustical transport techniques (Lighthill’s acoustic analogy, the Kirchhoff method, the Ffowcs Williams–Hawkings equation), linearized Euler approaches, combined procedures with CFD, semiempirical treatments like stochastic noise generation (SNGR), and even compressible direct numerical simulation (DNS) – admittedly very rarely used for acoustic analysis these days.

However, on artificial far-field boundaries, the physics dictates a straight pass-through without any spurious reflections. Although this requirement seems to be obvious, it is indeed very hard to fulfill sufficiently. Several concepts have been developed for this specific problem and optimized for one application or another, but the downside is that a generally accepted solution does not yet exist. Interior boundaries can be problematic as well. If we couple a CFD tool to a computational transport method, there is a difference between the models, and we may therefore obtain spurious reflections at the interface of the boundaries.

A more promising approach for technically relevant aeroacoustic problems is to apply hybrid methods. With this approach, the near-field aerodynamics are computed to obtain velocity and pressure fluctuations that form the acoustic source terms for a separate computation of the far-field acoustics. The reason for splitting off aerodynamics from aeroacoustics is the great disparity of levels and length scales between the flow and aeroacoustic fields. For both the simulation of the flow and the computation of the sound waves, a variety of methods exist that differ in accuracy and in their demand for computational resources.