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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 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. 

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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 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.140911.050412a}, url = {http://global-sci.org/intro/article_detail/cicp/7261.html} }
TY - JOUR T1 - Wave Propagation Across Acoustic/Biot's Media: A Finite-Difference Method AU - Guillaume Chiavassa & Bruno Lombard JO - Communications in Computational Physics VL - 4 SP - 985 EP - 1012 PY - 2013 DA - 2013/08 SN - 13 DO - http://doi.org/10.4208/cicp.140911.050412a UR - https://global-sci.org/intro/article_detail/cicp/7261.html KW - AB -

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. 

Guillaume Chiavassa and Bruno Lombard. (2013). Wave Propagation Across Acoustic/Biot's Media: A Finite-Difference Method. Communications in Computational Physics. 13 (4). 985-1012. doi:10.4208/cicp.140911.050412a
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