Séance Séminaire

Séminaire ACSIOM

On mathematical and numerical modelling of multiphysics wave propagation with polytopal Discontinuous Galerkin methods

In this talk, we focus on the numerical analysis of a polyhedral discontinuous Galerkin (PolyDG) scheme for the numerical simulation of multiphysics wave propagation in heterogeneous media. In particular, we address wave phenomena in poro-elasto-acoustic materials modeled by coupling the low-frequency Biot’s equations and the acoustics equations. 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 analyze the PolydG semi discrete formulation, which is then coupled with suitable time marching schemes. We point out that the geometric flexibility and the arbitrary-order accuracy featured by the proposed PolyDG method are fundamental as they ensure a high-level of precision and scalability that are needed to correctly represent the solutions. 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 investigate the performance of the proposed methods.