An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form

TL;DR

This paper introduces an energy-based discontinuous Galerkin method for simulating coupled elasto-acoustic wave equations, ensuring energy stability and high accuracy in fluid-solid interaction problems.

Contribution

The paper develops a novel energy-based DG scheme with provable stability and high order accuracy for coupled wave equations in fluid-solid media.

Findings

The scheme is energy stable with both energy conserving and upwind fluxes.

Numerical experiments confirm high accuracy and robustness.

The method effectively models wave propagation across fluid-solid interfaces.

Abstract

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.