High order discretization of seismic waves-problems based upon DG-SE methods

International audienceHybrid meshes comprised of hexahedras and te-trahedras are particularly interesting for representing media with local complex geometrical features like the seabed in offshore applications. We develop a coupled finite element method for solving elasto-acoustic wave equations. It combines Discontinuous Galerkin (DG) finite elements for solving elastodynamics with spectral finite elements (SE) for solving the acoustic wave equation. SE method has demonstrated very good performances in 3D with hexahedral meshes and contributes to reduce the computational burden by having less discrete unknowns than DG. The implementation of the method is performed both in 2D and 3D and it turns out that the coupling contributes to reduce the computational costs significantly: for the same time step and the same elementary mesh size, the CPU time of the coupled method is almost halved when compared to the one of a full DG method

A nodal discontinuous Galerkin finite element method for the poroelastic wave equation

We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated in the numerical scheme through an operator splitting approach. The well-posedness of the poroelastic system is proved by adopting an approach based on characteristic variables. An error analysis for a plane wave propagating in poroelastic media shows a convergence rate of O(hn+1). Computational experiments are shown for various combinations of homogeneous and heterogeneous poroelastic media