A time-domain numerical modeling of two-dimensional wave propagation in ă porous media with frequency-dependent dynamic permeability

Abstract : An explicit finite-difference scheme is presented for solving the ă two-dimensional Biot equations of poroelasticity across the full range ă of frequencies. The key difficulty is to discretize the ă Johnson-Koplik-Dashen (JKD) model which describes the viscous ă dissipations in the pores. Indeed, the time-domain version of Biot-JKD ă model involves order 1/2 fractional derivatives which amount to a time ă convolution product. To avoid storing the past values of the solution, a ă diffusive representation of fractional derivatives is used: The ă convolution kernel is replaced by a finite number of memory variables ă that satisfy local-in-time ordinary differential equations. The ă coefficients of the diffusive representation follow from an optimization ă procedure of the dispersion relation. Then, various methods of ă scientific computing are applied: The propagative part of the equations ă is discretized using a fourth-order finite-difference scheme, whereas ă the diffusive part is solved exactly. An immersed interface method is ă implemented to discretize the geometry on a Cartesian grid, and also to ă discretize the jump conditions at interfaces. Numerical experiments are ă proposed in various realistic configurations. (C) 2013 Acoustical ă Society of America.
Type de document :
Article dans une revue
Journal of the Acoustical Society of America, Acoustical Society of America, 2013, 134 (6, 2, SI), pp.4610-4623. 〈10.1121/1.4824832〉
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Soumis le : vendredi 10 février 2017 - 14:16:04
Dernière modification le : lundi 4 mars 2019 - 14:04:22

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Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. A time-domain numerical modeling of two-dimensional wave propagation in ă porous media with frequency-dependent dynamic permeability. Journal of the Acoustical Society of America, Acoustical Society of America, 2013, 134 (6, 2, SI), pp.4610-4623. 〈10.1121/1.4824832〉. 〈hal-01464730〉

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