  The aim of this work is to introduce and analyze a finite element
discontinuous Galerkin method on polygonal meshes for the numerical
discretization of acoustic waves propagation through poroelastic materials.
Wave propagation is modeled by the acoustics equations in the acoustic domain
and the low-frequency Biot's equations in the poroelastic one. The coupling is
realized by means of (physically consistent) transmission conditions, imposed
on the interface between the domains, modeling different pore configurations.
For the space discretization, we introduce and analyze a high-order
discontinuous Galerkin method on polygonal and polyhedral meshes, which is then
coupled with Newmark-$\beta$ time integration schemes. Stability analysis for
both the continuous and semi-discrete problem is presented and error estimates
for the energy norm are derived for the semi-discrete one. A wide set of
numerical results obtained on test cases with manufactured solutions are
presented in order to validate the error analysis. Examples of physical
interest are also presented to investigate the capability of the proposed
methods in practical scenarios.
