Atlantis Studies in Differential Equations

Mathematical Models for Poroelastic Flows

Authors: Meirmanov, Anvarbek

  • For each underground physical process the reader finds a set of mathematical models depending on the dimensionless criteria of the given process and describing the process with different degrees of exactness
  • The reader may apply the suggested approach to solve many other important problems in filtration and acoustics and obtain macroscopic mathematical models, which are asymptotically exact
  • First volume in a new series
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  • ISBN 978-94-6239-015-7
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About this book

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.

Table of contents (11 chapters)

  • Isothermal Liquid Filtration

    Meirmanov, Anvarbek

    Pages 1-65

  • Filtration of a Compressible Thermo-Fluid

    Meirmanov, Anvarbek

    Pages 67-87

  • Hydraulic Shock in Incompressible Poroelastic Media

    Meirmanov, Anvarbek

    Pages 89-134

  • Double Porosity Models for a Liquid Filtration

    Meirmanov, Anvarbek

    Pages 135-167

  • Filtration in Composite Incompressible Media

    Meirmanov, Anvarbek

    Pages 169-239

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-94-6239-015-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-94-6239-014-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Models for Poroelastic Flows
Authors
Series Title
Atlantis Studies in Differential Equations
Series Volume
1
Copyright
2014
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the authors
eBook ISBN
978-94-6239-015-7
DOI
10.2991/978-94-6239-015-7
Hardcover ISBN
978-94-6239-014-0
Series ISSN
2214-6253
Edition Number
1
Number of Pages
XXXVIII, 449
Number of Illustrations and Tables
22 b/w illustrations, 3 illustrations in colour
Topics