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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2015013278
pages 375-392

GENERAL INTEGRAL EQUATIONS OF STOKES FLOW THROUGH THE RANDOM STRUCTURE POROUS MEDIA

Valeriy A. Buryachenko
Civil Engineering Department, University of Akron, Akron, Ohio 44325-3901, USA and Micromechanics and Composites LLC, 2520 Hingham Lane, Dayton, Ohio 45459, USA

ABSTRACT

One considers a slow linear flow through a fixed random bed of rigid particles. The general integral equations (GIEs) connecting the fields of velocities and pressures of fluid in a point being considered and the fields in the surrounding points are obtained for the random (statistically homogeneous and inhomogeneous, so-called graded) structures containing the particles of arbitrary shape and orientation. The new GIEs are presented in a general form of perturbations introduced by the heterogeneities. The mentioned perturbations can be found by any available numerical method which has advantages and disadvantages; if it is crucial for the analyst to be aware of their range of applications. The method of obtaining GIEs is based on a centering procedure of subtraction from both sides of a new initial integral equation, their statistical averages obtained without any auxiliary asymptotic assumptions, which are exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs and establishes an advantage with the known GIEs.


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