Acoustic Relaxation Term for Damping and Forcing of Waves

An acoustic relaxation term for the momentum equation is introduced that can act as a damping or forcing term for pressure waves while leaving other modes untouched. This acoustic relaxation term can be seen as the acoustic variant of the eddy relaxation term previously introduced in other work, and therefore shares several important characteristics. Its damping behavior is shown to be favorably frequency selective; that is, application to a test case with spurious acoustics shows that, indeed, the acoustic relaxation term is able to remove these undesired oscillations while leaving the hydrodynamics untouched. Subsequently, the acoustic relaxation term is applied as a forcing to couple an acoustic signal into a computational aeroacoustics (CAA) simulation. The transfer function shows a desirable behavior. The acoustic relaxation term is able to damp or excite acoustic waves; in that way, it potentially enables the excitement of prescribed acoustics in the linearized equations, such as a linearized Euler or acoustic perturbation or, as is done in this paper, the Navier–Stokes equations.