Numerical modelling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods

TL;DR

This paper develops and analyzes a high-order discontinuous Galerkin method for simulating wave propagation in thermo-poroelastic media, supporting complex grids and providing stability and error estimates.

Contribution

It introduces a novel high-order DG scheme for thermo-poroelastic wave modeling with stability analysis and error estimates, and compares it with poroelastic models.

Findings

Numerical simulations verify theoretical error estimates.

The scheme effectively models wave propagation in thermo-poroelastic media.

Comparison highlights differences between thermo-poroelastic and poroelastic models.

Abstract

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and $hp$-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$\beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models.