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Title: A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

Abstract

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case.more » Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.« less

Authors:
 [1];  [1];  [1]
  1. Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712 (United States)
Publication Date:
OSTI Identifier:
21418123
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 229; Journal Issue: 24; Other Information: DOI: 10.1016/j.jcp.2010.09.008; PII: S0021-9991(10)00502-4; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANALYTICAL SOLUTION; CONVERGENCE; EXACT SOLUTIONS; NUMERICAL SOLUTION; SEISMIC WAVES; THREE-DIMENSIONAL CALCULATIONS; WAVE EQUATIONS; WAVE PROPAGATION; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Wilcox, Lucas C., E-mail: lucas@hypercomp.ne, Stadler, Georg, Burstedde, Carsten, Ghattas, Omar, Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712, and Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712. A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. United States: N. p., 2010. Web. doi:10.1016/j.jcp.2010.09.008.
Wilcox, Lucas C., E-mail: lucas@hypercomp.ne, Stadler, Georg, Burstedde, Carsten, Ghattas, Omar, Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712, & Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712. A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. United States. https://doi.org/10.1016/j.jcp.2010.09.008
Wilcox, Lucas C., E-mail: lucas@hypercomp.ne, Stadler, Georg, Burstedde, Carsten, Ghattas, Omar, Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712, and Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712. Fri . "A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media". United States. https://doi.org/10.1016/j.jcp.2010.09.008.
@article{osti_21418123,
title = {A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media},
author = {Wilcox, Lucas C., E-mail: lucas@hypercomp.ne and Stadler, Georg and Burstedde, Carsten and Ghattas, Omar and Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712 and Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712},
abstractNote = {We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.},
doi = {10.1016/j.jcp.2010.09.008},
url = {https://www.osti.gov/biblio/21418123}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 24,
volume = 229,
place = {United States},
year = {2010},
month = {12}
}