Mimicking a perfectly matched layer with a porous medium

The possibility of designing a porous medium that mimics an acoustical 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 V. E. Ostashev and D. K. 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 range of frequencies. For relatively high frequencies, however, it is shown that by setting the ratio of the vorticity and entropy shape factors to (Npr)1/2 /(γ-1), where Npr is the Prandtl number and γ is the ratio of specific heats, the impedance becomes real-valued while the medium remains attenuative. Possible approaches are discussed for adjusting this ratio based on varying the pore shape, the cross section, and the pore-size distribution. However, it does not appear to be possible to make the ratio less than one, as would be necessary to realize the PML condition in air and other fluids.The possibility of designing a porous medium that mimics an acoustical 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 V. E. Ostashev and D. K. 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 range of frequencies. For relatively high frequencies, however, it is shown that by setting the ratio of the vorticity and entropy shape factors to (Npr)1/2 /(γ-1), where Npr is the Prandtl number and γ is the ratio of specific heats, the impedance becomes real-valued while the medium remains attenuative. Possible approaches are discussed for adjusting this ratio based on varying the pore shape, the cross section, and the pore-size distribution. However, it does not appear to be possible to make the ra...