Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces
Résumé
This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity–stress and velocity–strain wave formulations are considered. The proposed approach allows the derivation of upwind numerical fluxes in a well structured and hierarchical way according to the degree of inhomogeneity across a physical interface. The numerical fluxes that are exact solutions of a relevant Riemann problem defined at a physical interface are obtained. The developed explicit and intrinsic tensorial expressions of upwind numerical fluxes in multidimensional case allow a better understanding and analysis of the physical meaning of involved terms. As numerical applications, an example with a physical interface separating two materials, one anisotropic and the other isotropic, and an example of polycrystalline material that presents a particular case with a larger number of physical interfaces, are considered. The proposed numerical fluxes are numerically investigated and validated.
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