Discontinuous Galerkin Method With a Novel Physics-Informed Flux for Elastic Wave Simulations in Heterogeneous Media

We present an innovative physics-informed numerical flux within the framework of the discontinuous Galerkin (DG) method for solving elastic wave equations in 2-D heterogeneous media that include interfaces between elastic materials. The first-order velocity-stress equations are used, which can be written in the formulation of hyperbolic system and can be easily incorporated into the framework of DG method. Numerical flux is carefully proposed to maintain the physical laws on both sides of the interface where material parameters are discontinuous. We compare the newly suggested numerical flux with both the classic local Lax-Friedrichs flux and the exact upwind flux. The latter is derived from solving the Riemann problem and adheres to the Rankine-Hugoniot condition. In the comparison, we find that our flux is formally similar to the classic local Lax-Friedrichs flux, but the numerical behavior is different from it; its numerical performance is similar to the exact upwind flux. The biggest advantage of the numerical flux we propose is that it does not need to accurately solve the Riemann problem, but it can maintain the physical continuity conditions near the interface with material discontinuities. We present three numerical examples of elastic wave propagation in heterogeneous media, including horizontal and inclined interfaces, and the Marmousi model. The numerical results demonstrate the effectiveness of this flux.