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Journal Articles Journal of the Acoustical Society of America Year : 2013

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

Abstract

An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amounts to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: the propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.
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Dates and versions

hal-00736757 , version 1 (29-09-2012)

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Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability. Journal of the Acoustical Society of America, 2013, 134 (6), pp.4610-4623. ⟨10.1121/1.4824832⟩. ⟨hal-00736757⟩
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