Abstract
We present a high-order discontinuous Galerkin method for the simulation of P-SV seismic wave propagation in heterogeneous media and two dimensions of space. The first-order velocity-stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress-strain relation in the time domain being a convolution, which is numerically intractable, we consider the rheology of a generalized Maxwell body replacing the convolution by differential equations. This results in a velocity-stress system which contains additional equations for the anelastic functions including the strain history of the material. Our numerical method, suitable for complex triangular unstructured meshes, is based on a centered numerical flux and a leap-frog time-discretization. The extension to high order in space is realized by Lagrange polynomial functions, defined locally on each element. The inversion of a global mass matrix is avoided since an explicit scheme in time is used. The method is validated through numerical simulations including comparisons with a finite difference scheme.
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Acknowledgements
The authors acknowledge the CETE Méditerranée – LRPC de Nice for its collaboration and support, and thank, in particular, E. Bertrand for providing the geotechnical model of Nice and the results of the related site effect assessment. The PhD fellowship of Fabien Peyrusse is funded by Région Provence-Alpes-Côte d’Azur and Ifsttar.
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Peyrusse, F., Glinsky, N., Gélis, C., Lanteri, S. (2014). A High-Order Discontinuous Galerkin Method for Viscoelastic Wave Propagation. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_29
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DOI: https://doi.org/10.1007/978-3-319-01601-6_29
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