Dispersion-dissipation analysis of triangular numerical-flux-based discontinuous Galerkin method for elastic wave equations

This paper presents a quantitative dispersion-dissipation and stability analysis of the triangle-based discontinuous Galerkin method (DGM) for simulating elastic wave propa-gation. The analysis is carried out for both P- and S-waves, with semi-discrete and fully discrete cases. The DGM is based on the 1st-order hyperbolic system with numerical flux formulations. The semi-discrete analysis is considered with respect to different numer-ical fluxes, different mesh configurations, and various ratios of P-wave velocity (V-p) and S-wave velocity (V-s). The LLF numerical flux and Godunov numerical flux are employed for the analysis. We consider two triangular mesh configurations, which are compared with the quadrilateral mesh. A fully discrete analysis is also presented where 3rd-order total variation diminishing Runge-Kutta temporal discretization is used. The results demonstrate that the numerical dispersion and dissipation vary significantly with the mesh configura-tions, but they show small difference with respect to the V-p/V-s values. In addition, the performance of LLF flux is similar to that of Godunov flux. (C) 2020 Elsevier Inc. All rights reserved.