title: 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 amount 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.
authors: Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France.
authors: Emilie
authors: E
authors: Blanc
authors: Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France.
authors: Guillaume
authors: G
authors: Chiavassa
authors: Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France.
authors: Bruno
authors: B
authors: Lombard