Section: New Results
Discontinuous Galerkin methods for the elastodynamic equations
DGTD-
method for the elastodynamic equations
Participants : Nathalie Glinsky-Olivier, Loula Fezoui.
We continue developing high order non-dissipative discontinuous
Galerkin methods on simplicial meshes (triangles in the 2D case and
tetrahedra in the 3D case) for the numerical solution of the first
order hyperbolic linear system of elastodynamic equations. These
methods share some ingredients of the DGTD- methods
developed by the team for the time domain Maxwell equations among
which, the use of nodal polynomial (Lagrange type) basis functions, a
second order leap-frog time integration scheme and a centered scheme
for the evaluation of the numerical flux at the interface between
neighboring elements. The resulting DGTD- methods have
been validated and evaluated in detail in the context of propagation
problems in both homogeneous and heterogeneous media including
problems for which analytical solutions can be computed. Particular
attention was given to the study of the mathematical properties of
these schemes such as stability, convergence and dispersion.
In the 2D case, the source modeling has been studied via the Garvin
test case i.e the propagation of an explosive source in a half-space
with a free surface. A class of high order leap-frog schemes has also
been studied. These schemes improve the accuracy of the highest
orders spatial schemes (for p
3 ) while being efficient since they
allow the use of larger time steps as compared to the
DGTD- method based on the second order leap-frog scheme.
Moreover, a preliminary study of site effects has been realised on a realistic topography of the Rognes area (south of France) where one of the strongest historical earthquake occured in 1909. The objective of this study was to analyze the seismic response at the surface by measuring amplification and the concerned frequency range when considering a 2D profile (sourth-north profile with real topographic data) subject to a vertical P plane wave of central frequency varying from 0.2 to 10.0 Hz. The first results are encouraging and an extension of such a study to the three dimensional case including real source signals is underway and will permit a comparison with real seismic recordings (from the data base of CETE Méditérannée, Nice).
In the 3D case, in the framework of the ANR QSHA project, canonical problems are studied such as semi-spherical or ellipsoidal canyon/basin in order to compare results of several numerical methods. More realistic test cases are examined via our participation to the Euroseistest Numerical Benchmark initiative. The objective of this benchmark, organized in the framework of the Cashima project (CEA Cadarache, the LGIT in Grenoble and Aristotle University of Thessaloniki), is to perform simulations of real events on the Volvi area (a well documented region near Thessaloniki) including complex characteristics of the medium.
