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

• Published in: Journal of computational physics 2010-12, Vol.229 (24), p.9373-9396
• Main Authors: Wilcox, Lucas C., Stadler, Georg, Burstedde, Carsten, Ghattas, Omar
• Format: Article
• Language: English
• Subjects: Computational techniques; Computer Science; Discontinuous Galerkin; Elastodynamic–acoustic interaction; Exact sciences and technology; Finite element method; Flux; Galerkin methods; h-Non-conforming mesh; High-order accuracy; Mathematical analysis; Mathematical methods in physics; Mathematical models; Media; Parallel computing; Physics; Three dimensional; Upwind numerical flux; Wave propagation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.09.008

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.