A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids

34/2020

A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids

Sunday 24th May 2020

Antonietti, P.F.; Botti, M.; Mazzieri, I.; Nati Poltri, S.

The aim of this work is to introduce a discretization of the physical phenomenon of propagation of acoustic waves through poroelastic materials, by exerting a finite element discontinuous Galerkin method on polygonal meshes. 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 introduced by considering (physically consistent) interface conditions, imposed on the interface between the domains, modelling both open and sealed pores. Existence and uniqueness is proven for the strong formulation based on employing the Hille-Yosida theorem. For the space discretization we introduce a discontinuous Galerkin method, which is then coupled with suitable time integration schemes, such as the leapfrog and the Newmark methods. A stability analysis both for the continuous problem and the semi-discrete one is presented and error estimates for the energy norm are derived. 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 test the capability of the proposed methods in practical cases.