Numerical tools were developed which are able to address acoustic wave propagation in dry and saturated porous media. Lattice methods, namely the lattice Boltzmann method (LBM) and the lattice spring model (LSM), can be successfully used for this purpose. The resulting code can upscale porous media properties or study direct time simulations in complex media. Only the second application is detailed here. Various media which contain or not a cavity, which possess uniform properties or not, which are flat or not are generated; an explosion is simulated and the accelerations are measured at the surface. The data show that when the medium is simple, the cavity can be easily located, which is not the case when it is random in volume or in surface.


Propagation of acoustic waves in saturated porous media is of large theoretical and practical interest in many areas of engineering. These studies were initiated by

Biot (1956a,b)

for low- and high-frequency acoustic waves propagating in a porous medium made of an elastic solid material saturated by a viscous compressible fluid.In order to avoid time dependence, the problem can be addressed by the homogenization theory

(Boutin and Auriault, 1990; Sanchez-Palencia, 1980)

in statistically homogeneous saturated porous media. A series of local problems defined on the unit cell are solved and the solutions are averaged over the unit cell in order to calculate the macroscopic parameters characterizing the porous medium, namely the effective stiffness tensor, the dynamic permeability, and the coefficients describing the reaction of the solid matrix to the fluid pressure. Then, the generalized Christoffel equation (

Malinouskaya, 2007

) is solved in order to calculate the macroscopic acoustic velocities. The three macroscopic propagation modes can be predicted.

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