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

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 $$\Omega _{\varepsilon }$$ Ω ε of thickness $$\varepsilon $$ ε which is perforated by periodically distributed solid cylinders of size $$a_\varepsilon $$ a ε . Generalizing (Anguiano and Suárez-Grau, ZAMP J Appl Math Phys 68:45, 2017), the fluid is described by the 3D incompressible Navier–Stokes system where the external force takes values in the space $$H^{-1}$$ H - 1 , and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude $$a_{\varepsilon }$$ a ε with respect to $$\varepsilon $$ ε . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

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

Loading next page...
 
/lp/springer_journal/the-transition-between-the-navier-stokes-equations-to-the-darcy-uTJvBeGybg
Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1086-z
Publisher site
See Article on Publisher Site

Abstract

We consider a Newtonian flow in a thin porous medium $$\Omega _{\varepsilon }$$ Ω ε of thickness $$\varepsilon $$ ε which is perforated by periodically distributed solid cylinders of size $$a_\varepsilon $$ a ε . Generalizing (Anguiano and Suárez-Grau, ZAMP J Appl Math Phys 68:45, 2017), the fluid is described by the 3D incompressible Navier–Stokes system where the external force takes values in the space $$H^{-1}$$ H - 1 , and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude $$a_{\varepsilon }$$ a ε with respect to $$\varepsilon $$ ε .

Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Feb 24, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off