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

Guillaume Chiavassa (1, 2) , Bruno Lombard (3)

1 ECM - École Centrale de Marseille
2 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
3 O&I - Ondes et Imagerie

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.

Mots clés: Biot's mode; poroelastic waves; jump conditions; imperfect hydraulic contact; high-order finite differences; immersed interface method

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Analyse numérique [math.NA]

Guillaume Chiavassa, Bruno Lombard. Wave propagation across acoustic / Biot's media: a finite-difference method. Communications in Computational Physics, 2013, 13 (4), pp.985-1012. ⟨10.4208/cicp.140911.050412a⟩. ⟨hal-00623627v2⟩