The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43956048" target="_blank" >RIV/49777513:23520/19:43956048 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.camwa.2019.04.004" target="_blank" >https://doi.org/10.1016/j.camwa.2019.04.004</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2019.04.004" target="_blank" >10.1016/j.camwa.2019.04.004</a>

Result language

angličtina

Original language name

The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling

Original language description

In this paper we present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels in a matrix made of a microporous material consisting of elastic skeleton and pores saturated by a viscous fluid. The macroscopic model is derived by the homogenization of the flow in the heterogeneous structure characterized by two small parameters involved in the two- level asymptotic analysis, whereby a scaling ansatz is adopted to respect the pore size differences. The first level upscaling of the fluid–structure interaction problem yields a Biot continuum describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model involving three equations for displacements, the mesoscopic flow velocity and the micropore pressure. Due to interactions between the two porosities, the macroscopic flow is governed by a Darcy–Brinkman model comprising two equations which are coupled with the overall equilibrium equation respecting the hierarchical structure of the two- phase medium. Expressions of the effective macroscopic parameters of the homogenized double-porosity continuum are derived, depending on the characteristic responses of the mesoscopic structure. Some symmetry and reciprocity relationships are shown and issues of boundary conditions are discussed. The model has been implemented in the finite element code SfePy which is well-suited for computational homogenization. A numerical example of solving a nonstationary problem using mixed finite element method is included.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20302 - Applied mechanics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Computers and Mathematics with Applications

ISSN

0898-1221

e-ISSN

—

Volume of the periodical

78

Issue of the periodical within the volume

9

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

23

Pages from-to

3044-3066

UT code for WoS article

000491624900014

EID of the result in the Scopus database

2-s2.0-85064837836