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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 and
Bruno Lombard
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
*
Corresponding author.Email:guillaume.chiavassa@centrale-marseille.fr
Email:lombard@lma.cnrs-mrs.fr
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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.

Keywords

35L0535L5065N0665N8574F10Biot’s modelporoelastic wavesjump conditionsimperfect hydraulic contacthigh-order finite differencesimmersed interface method

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Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 4 , April 2013, pp. 985 - 1012
Copyright
Copyright © Global Science Press Limited 2013

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