A Discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves

TL;DR

This paper presents a novel Discontinuous Galerkin method with modified penalty fluxes for simulating acousto-elastic wave propagation and scattering, including complex fluid-solid boundary interactions, ensuring stability and avoiding wave polarization diagonalization.

Contribution

The paper introduces a new DG approach with penalty flux modifications for stable simulation of anisotropic acousto-elastic waves and fluid-solid boundary interactions.

Findings

Stable algorithm for acousto-elastic wave simulation

Effective handling of fluid-solid boundary conditions

Avoids wave polarization diagonalization

Abstract

We develop an approach for simulating acousto-elastic wave phenomena, including scattering from fluid-solid boundaries, where the solid is allowed to be anisotropic, with the Discontinuous Galerkin method. We use a coupled first-order elastic strain-velocity, acoustic velocity-pressure formulation, and append penalty terms based on interior boundary continuity conditions to the numerical (central) flux so that the consistency condition holds for the discretized Discontinuous Galerkin weak formulation. We incorporate the fluid-solid boundaries through these penalty terms and obtain a stable algorithm. Our approach avoids the diagonalization into polarized wave constituents such as in the approach based on solving elementwise Riemann problems.