A stable and flexible discontinuous Galerkin (DG) method is proposed to simulate seismic wave propagation in heterogeneous media with solid-fluid interfaces. A key feature of this approach is the use of a modified numerical flux, which simplifies the treatment of solid-fluid interfaces. The main advantage of this numerical flux is that it does not need to accurately solve the Riemann problem, and can significantly reduce computational complexity while ensuring the preservation of physical relations, such as the continuity of normal traction and normal velocity, on both sides of acoustic-elastic interfaces where material parameters change discontinuously. For this method, a first-order velocity-pressure system is employed for the acoustic wave equation in the fluid, and a first-order velocity-stress system is employed for the elastic wave equation in the solid, which can be seamlessly integrated into the DG framework. Then the acoustic and elastic wave equations are coupled through this carefully designed numerical flux, ensuring physically accurate wavefield propagation across the fluid-solid interface. We compare our flux with the traditional exact upwind flux and the local Lax-Friedrichs (LLF) flux. The comparisons reveal that our flux shares similarities with the LLF flux in form, however, its numerical behavior closely resembles that of the exact upwind flux. The effectiveness of this proposed method is demonstrated via several numerical examples.
He et al. (Tue,) studied this question.