Numerical simulation of elastic wave propagation using a finite
volume method
Emmanuel Dormy and Albert Tarantola
Département de Sismologie, Institut de Physique du Globe de
Paris, France
Journal of Geophysical Research, Vol. 100, No. B2,
pp. 2123-2133.
Abstract. Like the finite difference method, the finite volume method gives an
approximate value for the derivative of a field at a given point
using the values of the field at a few locations neighboring the point.
The method uses the divergence theorem, considers a ``finite volume''
around the point and discretizes the surface bounding the volume.
When the considered finite volumes are regular polyhedra,
one obtains the expressions corresponding to standard centered finite
differences, but the finite volume method is more general than the
finite difference method because it may deal directly with irregular grids.
It is possible to give a finite volume formulation of the elastodynamic
problem, using dual volumes, that correspond, in the regular case, to the staggered grids used in the finite difference method.
The scheme thus obtained is more general than the one obtained using
finite differences, as the ``grids'' may be totally unstructured,
but at the cost of having, in the general case, only a first order accuracy.
Although the scheme is not consistent, numerical tests suggest that it
is stable and convergent.
This implementation of a finite volume method does not provide a way
for a more general treatment of the boundaries than the conventional
finite difference method.
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