Download RegSEM.u User Manual - Institut de Physique du Globe de Paris

Chapter 1
Mesh generation with CUBIT
The SEM is a finite element like method which involves the decomposition of the spatial domain into
non-overlapping elements, hexahedra at 3D. The generation of the mesh is the first step in a SEM modeling. It is particularly critical as it influences the accuracy of the propagated wave field and the stability
of the simulation. The particularity of RegSEM.u is its ability to handle 3D unstructured meshes. To
build these meshes, we use the CUBIT mesh generation toolkit (http://cubit.sandia.gov).
1.1
Conditions for the mesh definition
In order to make the SEM accurate and stable, all mesh should fulfill the two following important conditions, for the number of Gauss-Lobatto-Legendre (GLL) points which define the basis functions and
for the time step:
• To properly describe the seismic wave field, at least five GLL points per wavelength are needed
everywhere in the region. This means that the size of the elements d and the polynomial order N
are both constrained by the shortest wavelength λmin propagated in the medium. This condition
can be summarized by the following relation:
d≤
N
λmin .
5
(1.1)
• To ensure the stability of the time-marching, the time-step ∆t of the finite difference scheme has
to verify the Courant-Friedrichs-Lewy (CFL) condition:
∆x
∆t ≤ C
α
,
(1.2)
min
where C denotes the Courant number, usually chosen between 0.3 and 0.4, and ∆x
α min the
minimum ratio of grid spacing (distance between two GLL nodes) and P-wave speed.
1.2
Generation of the mesh files
CUBIT is a geometry and mesh generation toolkit developed by Sandia National Laboratories. It can
be purchased at a small cost for academic purposes. Considering the limited choice of commercial and