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

Published online by Cambridge University Press:  03 June 2015

Guillaume Chiavassa*
Affiliation:
Centrale Marseille, Laboratoire de Mecanique Modelisation et Procedes Propres, UMR 7340 CNRS, Technopole de Chateau-Gombert, 38 rue Frederic Joliot-Curie, 13451 Marseille, France
Bruno Lombard*
Affiliation:
Laboratoire de Mecanique et d’Acoustique, UPR 7051 CNRS, 31 chemin Joseph Aiguier, 13402 Marseille, France
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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