Multiscale simulation of acoustic waves in homogenized heterogeneous porous media with low and high permeability contrasts

Abstract

Acoustic behavior of fluid saturated, heterogeneous, rigid porous media which consist of two micro-porous materials with high permeability contrast is studied using a two-scale model based on the homogenization theory. At the mesoscopic level, the fluid motion is governed by the generalized Darcy flow model. At the macroscopic scale, effective acoustic properties are described by a model which has recently been derived using the periodic unfolding method (Rohan, 2013).This paper presents a computational procedure for estimating the pressure and the velocity fields at both the mesoscale and the macroscale. The model is validated by comparing the multiscale solutions with those of the model with exact periodic mesostructural geometry. The numerical solutions are computed via the finite element method. The ranges of applicability of homogenized models with “high contrast” and “low contrast” permeabilities are also investigated.