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Über dieses Buch

The The book book was was planned planned in in such such a a manner manner that that two two basic basic goals goals would would be be reached. reached. On On the the one one hand, hand, the the goal goal was was to to show show some some new new results results in in the the field field of of modeling modeling transport transport through through highly highly heterogeneous heterogeneous media, media, based based on on the the homogenization homogenization theory. theory. Multiple Multiple new new mathematical mathematical models models of of transport transport are are presented presented herein, herein, studying studying their their properties, properties, developing developing methods methods to to compute compute effective effective parameters parameters of of the the averaged averaged media, media, simulation simulation of of cell cell problems, problems, using using new new models models to to simulate simulate some some practical practical problems. problems. High High heterogeneity heterogeneity being being subjected subjected to to the the homogenization homogenization procedure, procedure, generates generates non-local non-local phenomena phenomena and and then then gives gives a a possibility possibility to to develop develop a a new, new, non-local non-local (or (or "dynamic"), "dynamic"), theory theory of of transport transport in in porous porous media. media.

Inhaltsverzeichnis

Frontmatter

1. One Phase Darcy’s Flow In Double Porosity Media

Abstract
The basic object of examination of this book is associated with highly heterogeneous media where the permeability is contrasting in various elements of the domain. Construction of the averaged models in this case requires to solve several specific basic problems, as determination of the averaging method and a priori classification of media allowing to obtain constructive results of homogenization.
Mikhail Panfilov

2. Chemical or Heat Convection-Diffusion Transport Through Highly Heterogeneous Porous Media

Abstract
The next step of the developed theory is related with the flow of miscible mixtures. The linear convection-diffusion equation written relatively to the concentration of a chemical component is a simplest model of mixture flow. In this chapter a more general model is studied when the field of convection transport velocity is not given and should be found as the solution of a parabolic equation for the velocity potential (the pressure).
Mikhail Panfilov

3. Dispersion Tensor in Anisotropic Network Media. Stream Configuration Method

Abstract
Calculation of the effective dispersion tensor is one of the basic problems in the theory of chemical or heat transport through heterogeneous media. A number of paper was devoted to this problem using various mathematical approaches. A review of the results obtained may be found in the book of P.Adler, 1991 (see list of references at the end of chapter 2).
Mikhail Panfilov

4. Two-Phase Flow in Double Porosity Media

Abstract
Problem of upscaling two-phase flow through highly heterogeneous media deals with a more complex case of transport equations, characterized by nonlinearity and degeneration of relative permeabilities, as well as by specific capillary phenomena which determine discontinuous behavior of the saturation, that has not anything similar in linear case.
Mikhail Panfilov

5. Two-Phase Flow in Pseudo-Cavity Media

Abstract
In this chapter, another class of media will be studied, which is ”inverse” respectively to the objects examined in all the previous chapters.
Mikhail Panfilov

Backmatter

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