Volume 13, Issue 4
Wave Propagation Across Acoustic/Biot's Media: a Finite-difference Method

Guillaume Chiavassa & Bruno Lombard

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

Published online: 2013-08

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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 timemarching; 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. 

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@Article{CiCP-13-985, author = {Guillaume Chiavassa and Bruno Lombard}, title = {Wave Propagation Across Acoustic/Biot's Media: a Finite-difference Method}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {4}, pages = {985--1012}, 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 timemarching; 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.140911.050412a}, url = {http://global-sci.org/intro/article_detail/cicp/7261.html} }
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