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

International audienceAn 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