The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium

We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the...

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Autores: Anguiano Moreno, María, Suárez Grau, Francisco Javier
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/157536
Acesso em linha:https://hdl.handle.net/11441/157536
https://doi.org/10.1007/s00009-018-1086-z
Access Level:acceso abierto
Palavra-chave:Homogenization
Navier-Stokes equations
Darcy’s law
porous medium
thin-film fluids.
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spelling The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous MediumAnguiano Moreno, MaríaSuárez Grau, Francisco JavierHomogenizationNavier-Stokes equationsDarcy’s lawporous mediumthin-film fluids.We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By means of an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude aε with respect to ε.Junta de Andalucía P12-FQM-2466Ministerio de Economía y Competitividad MTM2014-53309-PSpringerAnálisis MatemáticoJunta de AndalucíaMinisterio de Economía y Competitividad (MINECO). España2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/157536https://doi.org/10.1007/s00009-018-1086-zreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésP12-FQM-2466MTM2014-53309-Phttps://doi.org/10.1007/s00009-018-1086-zinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1575362026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
title The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
spellingShingle The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
Anguiano Moreno, María
Homogenization
Navier-Stokes equations
Darcy’s law
porous medium
thin-film fluids.
title_short The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
title_full The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
title_fullStr The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
title_full_unstemmed The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
title_sort The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
dc.creator.none.fl_str_mv Anguiano Moreno, María
Suárez Grau, Francisco Javier
author Anguiano Moreno, María
author_facet Anguiano Moreno, María
Suárez Grau, Francisco Javier
author_role author
author2 Suárez Grau, Francisco Javier
author2_role author
dc.contributor.none.fl_str_mv Análisis Matemático
Junta de Andalucía
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Homogenization
Navier-Stokes equations
Darcy’s law
porous medium
thin-film fluids.
topic Homogenization
Navier-Stokes equations
Darcy’s law
porous medium
thin-film fluids.
description We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By means of an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude aε with respect to ε.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/157536
https://doi.org/10.1007/s00009-018-1086-z
url https://hdl.handle.net/11441/157536
https://doi.org/10.1007/s00009-018-1086-z
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv P12-FQM-2466
MTM2014-53309-P
https://doi.org/10.1007/s00009-018-1086-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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