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A Highly Accurate Discontinuous Galerkin Method for Complex Interfaces Between Solids and Moving Fluids

Käser, Martin, and Michael Dumbser (2008), A Highly Accurate Discontinuous Galerkin Method for Complex Interfaces Between Solids and Moving Fluids, Geophysics, 73(3), T23-T35, doi:10.1190/1.2870081.

Abstract
We present a new highly accurate numerical scheme for unstructured two- and three-dimensional meshes based on the Discontinuous Galerkin approach to simulate seismic wave propagation in heterogeneous media containing fluid-solid interfaces. Due to the formulation of the wave equations as a first order hyperbolic system in velocity-stress, the fluid may also be in movement along the interface. The Discontinuous Galerkin approach allows for jumps of the material parameters and the solution across element interfaces, which are handled by so-called Riemann solvers or numerical fluxes. The use of Riemann solvers at the element interfaces makes the treatment of the fluid particularly simple by setting the shear modulus in the fluid region to zero. No additional compatibility relations such as vanishing shear stress or continuity of normal stresses are necessary in order to couple the solid and the fluid along an interface. The Riemann solver automatically recognizes the jump of the material coefficients at the interface and provides the correct numerical fluxes for fluid-solid contacts. Therefore, wave propagation in the entire computational domain containing heterogeneous media of an acoustic fluid and an elastic solid can be described by the uniform set of the elastic wave equations. In the case of a moving fluid the convection velocity can simply be overlaid. The accuracy of the proposed scheme is confirmed by comparing numerical results against analytical solutions. Finally, the new method is applied to a three-dimensional model problem of marine seismic exploration
with a fluid-solid interface determined by a complicated ocean bottom topography.
BibTeX
@article{id714,
  author = {Martin K{\"a}ser and Michael Dumbser},
  journal = {Geophysics},
  number = {3},
  pages = {T23-T35},
  title = {{A Highly Accurate Discontinuous Galerkin Method for Complex Interfaces Between Solids and Moving Fluids}},
  volume = {73},
  year = {2008},
  doi = {10.1190/1.2870081},
}
EndNote
%0 Journal Article
%A Käser, Martin
%A Dumbser, Michael
%D 2008
%N 3
%V 73
%J Geophysics
%P T23-T35
%T A Highly Accurate Discontinuous Galerkin Method for Complex Interfaces Between Solids and Moving Fluids
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