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Composites: Mechanics, Computations, Applications: An International Journal
ESCI SJR: 0.193 SNIP: 0.497 CiteScore™: 0.39

ISSN Print: 2152-2057
ISSN Online: 2152-2073

Composites: Mechanics, Computations, Applications: An International Journal

DOI: 10.1615/CompMechComputApplIntJ.v6.i3.50
pages 239-264

BRINKMAN'S FILTRATION OF FLUID IN RIGID POROUS MEDIA: MULTISCALE ANALYSIS AND INVESTIGATION OF EFFECTIVE PERMEABILITY

Viktoria Savatorova
Central Connecticut State University
Alexey Talonov
UNLV, MEPhI
A. N. Vlasov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russian Federation
Dmitriy B. Volkov-Bogorodsky
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russia

ABSTRACT

A homogenization procedure was implemented to carry out a multiscale asymptotic analysis of Brinkman's filtration of fluid in rigid porous media. As a result we obtained averaged macroscopic equations with the components of the effective permeability tensor as effective coefficients. The derivation of the components of the effective permeability tensor was reduced to the solution of periodic boundary problems in a unit cell. In order to solve this problem we have developed an analytical-numerical method based on approximation of the solution by the series of shape functions that exactly satisfied the interface conditions on the boundaries between different phases of flow. For some specific elements of a periodic pore structure, the shape functions can be obtained in a closed analytical form. This enables ones to monitor the accuracy of the cell problem solution. We have solved the cell problem in 1D and 3D formulations and provided a comparison of the effective permeability coefficients, computed analytically and numerically for both Brinkman's and Stokes' filtration for different cases of a microscopic pore structure. The results of the cell problem solution have been subsequently used in the integration of the averaged macroscopic equations for determining the distribution of fluid pressure and velocity.


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