Mathematical Models for Poroelastic Flows

✍ Scribed by Anvarbek Meirmanov (auth.)

• Publisher: Atlantis Press
• Year: 2014
• Tongue: English
• Leaves: 477
• Series: Atlantis Studies in Differential Equations 1
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xxxviii
Isothermal Liquid Filtration....Pages 1-65
Filtration of a Compressible Thermo-Fluid....Pages 67-87
Hydraulic Shock in Incompressible Poroelastic Media....Pages 89-134
Double Porosity Models for a Liquid Filtration....Pages 135-167
Filtration in Composite Incompressible Media....Pages 169-239
Isothermal Liquid Filtration....Pages 241-263
Non-isothermal Acoustics in Poroelastic Media....Pages 265-283
Isothermal Acoustics in Composite Media....Pages 285-316
Double Porosity Models for Acoustics....Pages 317-325
Diffusion and Convection in Porous Media....Pages 327-365
The Muskat Problem....Pages 367-381
Back Matter....Pages 383-449

✦ Subjects

Partial Differential Equations; Mathematical Methods in Physics; Mechanics