Mimicking a perfectly matched layer with a porous medium

The possibility of designing a porous medium that mimics a perfectly matched layer (PML) is discussed. In numerical methods, a PML provides essentially zero reflection and rapid attenuation in space. As a starting point to designing such a medium, the relaxation-model equations (10.54) and (10.55) from Ostashev and Wilson [Acoustics in Moving Inhomogeneous Media (CRC Press, Boca Raton, 2016)] are employed. In general, it does not appear to select the parameters to mimic a PML across a broad range of frequencies. For relatively high frequencies, however, it is shown that by setting the ratio of the vorticity and entropy shape factors to √N pr/(γ-1), where N pr is the Prandtl number and γ the ratio of specific heats, the impedance becomes real-valued while the medium remains attenuative. The reflected power is small provided that the porosity is close to one. It is unclear whether such media are physically realizable. Possible approaches to realization are discussed based on varying the pore shape, parallel configurations of pores with differing cross sections, and metamaterials.