An exact Riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling

Abstract

We present a nonconformal mesh discontinuous Galerkin pseudospectral time domain algorithm for arbitrary anisotropic elastic/acoustic wave propagation problems. An exact Riemann solver is compactly derived to resolve the accurate coupling of multiple domains in the discontinuous Galerkin framework, including heterogeneous anisotropic solid–solid, acoustic–acoustic, and anisotropic solid–fluid interactions. We simplify the eigenvalue problem in the Riemann solution from the rank of 9 to 3, and introduce the generalized wave impedance with more physical insight. Validations and verifications with independent codes and analytical solutions illustrate the accuracy, flexibility, and stability of our algorithm.