Double Porosity Models for Acoustics
Anvarbek Mukatovich Meirmanov · Atlantis studies in differential equations · 2013
Double porosity models for acoustics in poroelastic media is derived from homogenization theory. The fluid dynamics on the microscopic level is governed by the the nonstationary Stokes systems for a slightly compressible viscous liquid. The liquid domain is a union of two independent systems of fractures and pores. We suppose that the dimensionless size $$\varepsilon $$ of pores depends on the dimensionless size $$\delta $$ of cracks: $$\varepsilon =\delta ^{r}$$ with $$r>1$$ . The dynamics of a solid skeleton is described by the nonstationary Lamé’s system. The rigorous justification is fulfilled for homogenization procedure as the dimensionless size of the fractures tends to zero, while the solid body is geometrically periodic. To simplify the procedure we suppose that all solid blocks perforated with pores are already homogenized. As a result we derive the Biot’s like system of acoustics in poroelastic media.