An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form
This work provides a stable and accurate numerical method for simulating wave propagation in coupled fluid-solid regions, relevant to geophysics and engineering applications.
The paper develops an energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations, achieving provable energy stability and high-order accuracy. Numerical experiments demonstrate the scheme's accuracy and robustness.
We consider wave propagation in a coupled fluid-solid region, separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed, energy based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme.