Commun. Comput. Phys., 13 (2013), pp. 985-1012.


Wave Propagation Across Acoustic/Biot's Media: A Finite-Difference Method

Guillaume Chiavassa 1*, Bruno Lombard 2

1 Centrale Marseille, Laboratoire de Mecanique Modelisation et Procedes Propres, UMR 7340 CNRS, Technopole de Chateau-Gombert, 38 rue Frederic Joliot-Curie, 13451 Marseille, France.
2 Laboratoire de Mecanique et d'Acoustique, UPR 7051 CNRS, 31 chemin Joseph Aiguier, 13402 Marseille, France.

Received 14 September 2011; Accepted (in revised version) 5 April 2012
Available online 21 September 2012
doi:10.4208/cicp.140911.050412a

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-posedness 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.

AMS subject classifications: 35L05, 35L50, 65N06, 65N85, 74F10

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Key words: Biot's model, poroelastic waves, jump conditions, imperfect hydraulic contact, high-order finite differences, immersed interface method.

*Corresponding author.
Email: guillaume.chiavassa@centrale-marseille.fr (G. Chiavassa), lombard@lma.cnrs-mrs.fr (B. Lombard)
 

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