  In this work we review discontinuous Galerkin finite element methods on
polytopal grids (PolydG) for the numerical simulation of multiphysics wave
propagation phenomena in heterogeneous media. In particular, we address wave
phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave
propagation is modeled by using either the elastodynamics equation in the
elastic domain, the acoustics equations in the acoustic domain and the
low-frequency Biot's equations in the poro-elastic one. The coupling between
different models is realized by means of (physically consistent) transmission
conditions, weakly imposed at the interface between the subdomains. For all
models configuration, we introduce and analyse the PolydG semi-discrete
formulation, which is then coupled with suitable time marching schemes. For the
semi-discrete problem, we present the stability analysis and derive a-priori
error estimates in a suitable energy norm. A wide set of verification tests
with manufactured solutions are presented in order to validate the error
analysis. Examples of physical interest are also shown to demonstrate the
capability of the proposed methods.
