By Anvarbek Meirmanov

The publication is dedicated to rigorous derivation of macroscopic mathematical types as a homogenization of tangible mathematical versions on the microscopic point. the assumption is sort of normal: one first needs to describe the joint movement of the elastic skeleton and the fluid in pores on the microscopic point via classical continuum mechanics, after which use homogenization to discover applicable approximation versions (homogenized equations). The Navier-Stokes equations nonetheless carry at this scale of the pore dimension within the order of five – 15 microns. hence, as we've got pointed out above, the macroscopic mathematical versions bought are nonetheless in the limits of actual applicability. those mathematical versions describe diversified actual tactics of liquid filtration and acoustics in poroelastic media, akin to isothermal or non-isothermal filtration, hydraulic surprise, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our examine relies upon the Nguetseng two-scale convergent method.

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