Wave propagation in strongly heterogeneous fluid saturated porous medium: Asymptotic analysis and computational issues

Abstract eng:
We consider acoustic waves in fluid-saturated periodic media with different types of heterogeneity. At the mesoscopic level, the structure is periodic, consisting of two porous structures called matrix and channels with different characterization of their microscopic components. Models of rigid and deformable porous media are considered. For both these cases we present models with small and large contrasts in the permeability, called the “single” and the “double” porosity models, respectively. The two-scale homogenization method based on the asymptotic analysis of periodic structures was used to obtain the macroscopic models. To respect the large contrasts, the permeability and other poroelastic coefficients relevant to the mesoscopic level were scaled with respect to the size of the heterogeneity in the case of the double porosity models. We discus differences between the considered models. The dispersion curves illustrating the plane wave propagation were computed. It is possible to distinguish which model (single, or double porosity) should be used as a suitable approximation for a given specific contrast of the material properties.

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