Elasto-acoustic wave propagation in geophysical media using hybrid high-order methods on general meshes

TL;DR

This paper explores hybrid high-order methods for simulating coupled elasto-acoustic waves in geophysical media, demonstrating their accuracy, stability, and flexibility on complex meshes with efficient time discretization strategies.

Contribution

It introduces a novel application of HHO methods to elasto-acoustic wave problems with detailed analysis of explicit and implicit time schemes and their efficient implementation.

Findings

HHO methods achieve high accuracy on complex meshes.

Implicit schemes remain competitive with explicit ones.

Simulations validate geometrical flexibility and accuracy.

Abstract

Hybrid high-order (HHO) methods are numerical methods characterized by several interesting properties such as local conservativity, geometric flexibility and high-order accuracy. Here, HHO schemes are studied for the space semi-discretization of coupled elasto-acoustic waves in the time domain using a first-order formulation. Explicit and singly diagonal implicit Runge--Kutta (ERK & SDIRK) schemes are used for the time discretization. We show that an efficient implementation of explicit (resp. implicit) time schemes calls for a static condensation of the face (resp. cell) unknowns. Crucially, both static condensation procedures only involve block-diagonal matrices. Then, we provide numerical estimates for the CFL stability limit of ERK schemes and present a comparative study on the efficiency of explicit versus implicit schemes. Our findings indicate that implicit time schemes remain competitive in many situations. Finally, simulations in a 2D realistic geophysical configuration are performed, illustrating the geometrical flexibility of the HHO method: both hybrid (triangular and quadrilateral) and nonconforming (with hanging nodes) meshes are easily handled, delivering results of comparable accuracy to a reference spectral element software based on tensorized elements.