Isotropic Riemann Solver for a Nonconformal Discontinuous Galerkin Pseudospectral Time-Domain Algorithm

We present a discontinuous Galerkin pseudospectral time-domain (DG-PSTD) algorithm to solve elastic-/acoustic-wave propagation problems. The developed DG-PSTD algorithm combines the merits of flexibility from a finite-element method and spectral accuracy and efficiency from a high-order pseudospectral method, while having a flavor closer to a finite-volume method. This numerical approach not only uses structured/unstructured conformal meshes but also handles nonconformal meshes (h-adaptivity) with nonuniform approximation orders (p-adaptivity) in different regions, thus leading to high flexibility and efficiency for heterogeneous multiscale problems. To implement the discontinuous Galerkin algorithm, a concise but more general heterogeneous Riemann solver is provided to effectively and accurately resolve the coupling of multiple subdomains for both elastic-elastic/fluid-fluid and fluid-solid coupling. Finally, numerical results demonstrate the flexibility, high accuracy, and efficiency of our method for elastic-/acoustic-wave simulation.