Wave propagation across acoustic / Biot's media: a finite-difference method

TL;DR

This paper develops a finite-difference numerical method to simulate wave propagation in heterogeneous fluid and poroelastic media, incorporating interface conditions and capturing complex wave phenomena with high accuracy.

Contribution

It introduces a novel finite-difference approach combining ADER schemes, mesh refinement, and immersed interface methods for accurate wave simulation across fluid/poroelastic media.

Findings

Accurately models wave propagation in heterogeneous media.

Effectively captures interface effects with subcell resolution.

Demonstrates high accuracy through numerical experiments.

Abstract

Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-possedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time-marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot's theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.