AVERAGING OF THE SYSTEM OF EQUATIONS OF MOTION OF A VISCOUS-FLUID IN A POROUS-MEDIUM

A system of equations of motion of a viscous fluid (with a small coeff icient of viscosity) in a periodic porous medium is considered. The ra tio of the period of the structure of the medium to the characteristic dimension of the problem is a small parameter. The pore size and peri od of the structure are of the same order of magnitude. A formal asymp totic solution is constructed and an averaged equation, which is an an alogue of the Boussinesq equation, is derived.