# Abstract

__Viktoria Savatorova__: „Multi-scale modeling of filtration process through rigid porous medium”

National Research Nuclear University, Moscow, Russia

Asymptotical homogenization technique was applied for the flow of an incompressible and compressible barotropic fluid through a rigid porous medium with taking into account the fact that the viscosity of the fluid can depend on the pressure. As a special case we consider the flow of the fluid through a porous solid considering the latter as a system of parallel fibers. We derived analytical solution for a 1D flow of viscous fluid through a periodic system of thin parallel fibers. As another example we also consider a case of 3D flow through a sand soil. In this case the pore space is formed by grain boundaries. Numerical solutions were obtained for the effective permeability tensor, the fluid pressure and velocity.