NUMERICAL-SIMULATION OF ELASTIC-WAVE PROPAGATION USING A FINITE-VOLUME METHOD

Like the finite difference method, the finite volume method gives an a pproximate 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'' arou nd the point and discretizes the surface bounding the volume. When the finite volumes considered are regular polyhedra, one obtains the expr essions corresponding to standard centered finite differences, but the finite volume method is more general than the finite difference metho d 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 g rids 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 th e general case, only a first-order accuracy. Although the scheme is no t 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.