A nodal discontinuous Galerkin finite element method for the poroelastic wave equation
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We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated in the numerical scheme through an operator splitting approach. The well-posedness of the poroelastic system is proved by adopting an approach based on characteristic variables. An error analysis for a plane wave propagating in poroelastic media shows a convergence rate of O(hn+ 1). Computational experiments are shown for various combinations of homogeneous and heterogeneous poroelastic media.
KeywordsWaves Poroelasticity Lax-Friedrich Attenuation Numerical flux
Mathematics Subject Classification (2010)35L05 35S99 65M60 74J05 74J10 93C20
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KS would like to acknowledge the School of Geology, OSU and the MCSS, EPFL Switzerland, for providing the fund to carry out this work. We also acknowledge the OGS, Italy for hosting KS at various occasions. We thank editors and three anonymous reviewers for very useful comments. KS would like to acknowledge Sundeep Sharma at Devon Energy, for various discussions and proof-reading the manuscript. This is Boone Pickens School of Geology, Oklahoma State University, contribution number 2019-100.
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