Julien Diaz

We apply a hybridizable discontinuous Galerkin (HDG) method to numerically solve two‐dimensional anisotropic poroelastic wave equations in the frequency domain given by Biot theory. The motivation for choosing HDG method comes from the complexity of the considered equations and the high number of unknowns. The HDG method possesses all the advantages of discontinuous Galerkin method (hp‐adaptivity, accuracy, ability to model complex tectonics, etc.) without a drastic increase in the number of degrees of freedom. After a description of its implementation, we illustrate the accuracy of the proposed method by comparisons with analytical solutions. We then perform a sensitivity analysis of the method as a function of stabilization parameters and frequency, and show in particular that there exists optimal values of these parameters in order to obtain a very good level of accuracy. We also show the ability of the method to reproduce the different types of poroelastic waves including the slow Biot wave.

In this work, we have worked on possibilities to model artificial boundaries needed in the simulation of wave propagation in acoustic heterogeneous media. Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. Two possibilities were studied and compared in computational tests: the use of absorbing boundary conditions on an artificial boundary in the atmosphere layer and the elimination of the atmosphere layer using an equivalent boundary condition that mimics the propagation of waves through the atmosphere.

We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.

Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces - Volume 11 Issue 2 - Hélène Barucq, Julien Diaz, Véronique Duprat