  This paper deals with the numerical modeling of wave propagation in porous
media described by Biot's theory. The viscous efforts between the fluid and the
elastic skeleton are assumed to be a linear function of the relative velocity,
which is valid in the low-frequency range. The coexistence of propagating fast
compressional wave and shear wave, and of a diffusive slow compressional wave,
makes numerical modeling tricky. To avoid restrictions on the time step, the
Biot's system is splitted into two parts: the propagative part is discretized
by a fourth-order ADER scheme, while the diffusive part is solved analytically.
Near the material interfaces, a space-time mesh refinement is implemented to
capture the small spatial scales related to the slow compressional wave. The
jump conditions along the interfaces are discretized by an immersed interface
method. Numerical experiments and comparisons with exact solutions confirm the
accuracy of the numerical modeling. The efficiency of the approach is
illustrated by simulations of multiple scattering.
