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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Computers and Mathematics with Applications

ISSN

0898-1221

e-ISSN

—

Svazek periodika

78

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

3044-3066

Kód UT WoS článku

000491624900014

EID výsledku v databázi Scopus

2-s2.0-85064837836