Hybrid high-order methods for elasto-acoustic wave propagation in the time domain

TL;DR

This paper introduces a Hybrid High-Order (HHO) method for simulating coupled acoustic and elastic wave propagation in the time domain, providing stability, accuracy, and mesh independence for complex media.

Contribution

The paper develops a novel HHO method with stability analysis and optimal convergence rates for elasto-acoustic wave coupling in the time domain.

Findings

Energy-error estimates established for the method.

O(1)-stabilization avoids excessive CFL restrictions.

Optimal convergence rates of order (k+1) and (k+2) achieved.

Abstract

We devise a Hybrid High-Order (HHO) method for the coupling between the acoustic and elastic wave equations in the time domain. A first-order formulation in time is considered. The HHO method can use equal-order and mixed-order settings with polynomial degree k>=0 for the face unknowns, together with O(1)- and O(1/h)-stabilizations. An energy-error estimate is established in the time-continuous case. A numerical spectral analysis is performed, showing that O(1)-stabilization is required to avoid excessive CFL limitations for explicit time discretizations. Moreover, the spectral radius of the stiffness matrix is fairly independent of the geometry of the mesh cells. For analytical solutions on general meshes, optimal convergence rates of order (k+1) are shown in both equal- and mixed-order settings using O(1)-stabilization, whereas order (k+2) is achieved in the mixed-order setting using O(1/h)-stabilization. Test cases with a Ricker wavelet as an initial condition showcase the relevance of the proposed method for the simulation of elasto-acoustic wave propagation across media with contrasted material properties.