Well-posed Perfectly Matched Layers for Advective Acoustics

Using a mathematical framework originally developed for the development of PML schemes in computational electromagnetics, we develop a set of strongly well-posed PML equations for the absorption of acoustic and vorticity waves in two-dimensional convective acoustics under the assumption of a spatially constant mean flow. A central piece in this development is the development of a variable transformation that conserves the dispersion relation of the physical space equations. The PML equations are given for layers being perpendicular to the direction of the mean flow as well as for layers being parallel to the mean flow. The efficacy of the PML scheme is illustrated by solving the equations of acoustics using a 4th order scheme, confirming the accuracy as well as stability of the proposed scheme.