Editor: Matthias Ehrhardt

Series Title: Progress in Computaional Physics (PiCP)

Coupled Fluid Flow in Energy, Biology and Environmental Research

Volume 2

eBook: US $24 Special Offer (PDF + Printed Copy): US $110
Printed Copy: US $98
Library License: US $96
ISSN: 1879-4661 (Print)
ISBN: 978-1-60805-691-0 (Print)
ISBN: 978-1-60805-254-7 (Online)
Year of Publication: 2012
DOI: 10.2174/97816080525471120101


Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications.

With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories.

In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume.

Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems.

The second volume of this series, titled Coupled Fluid Flow in Energy, Biology and Environmental Research covers the following scientific topics in the fields of modeling, numerical methods and applications:

  • - Coupling between free and porous media flow
  • - Coupling of flow and transport models
  • - Coupling of atmospheric and ground water models

This second volume contains both, the mathematical analysis of the coupling between fluid flow and porous media flow and state-of-the art numerical techniques, like tailor-made finite element and finite volume methods. Finally, readers will come across articles devoted to concrete applications of these models in the field of energy, biology and environmental research.

Indexed in: EBSCO, Ulrich's Periodicals Directory.


The mathematical analysis and numerical simulation of coupled flows in plain and porous media is of paramount importance for many current industrial and environmental problems such as proton exchange membrane (PEM) fuel cells, flow through oil filters, contaminant transport from lakes by groundwater, flow in bioreactors, contaminant gas leaking from atomic waste containers in deep rock depositories, CO sequestration in the subsurface, salt water intrusion and cancer therapy.

When using Navier-Stokes and Darcy’s equations to model flow in the two regions, finding effective coupling conditions at the interface between the fluid and the porous layer poses a challenge since the structures of the corresponding differential operators are different. However, when using the Generalized Model (Vafai and Tien, 1981) for the porous media, this difficulty does not occur, i.e. continuity of velocity and stress at the interface can be satisfied. Comprehensive modeling, conceptual set-up and assessment and applications of this approach has been shown in Vafai and Thiyagaraja (1987), Alazmi and Vafai (2001), Vafai and Kim (1990), Vafai and Huang (1994) and Huang and Vafai (1994).

There exists some well-known models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid-porous interface, like the Stokes/Brinkman problem with Ochoa-Tapia & Whitaker (1995) interface conditions and the Stokes/Darcy problem with Beavers & Joseph (1967) or Saffman (1971) conditions that have been shown to be well-posed. More recently, new coupling strategies were constructed using a transition region instead of a sharp interface, where the physical properties of the medium have a strong but still continuous variations. This approach was discussed by Nield (1983) and was developed e.g. by Goyeau et al. (2003), Chandesris & Jamet (2006), Hill & Straughan (2008) and Nield & Kuznetsov (2009).

At present, this research area is very attractive as shown by the active recent literature within several different journals. The book edited by Prof. Matthias Ehrhardt provides some particularly interesting keys to enter in this vast and exciting research domain of coupled fluid flow. By focusing on specific advanced subjects related to coupled flow problems from the different viewpoints of analysis, numerical techniques and practical applications with chapters written by distinguished experts in their respective fields, the reader will find an overview of state-of-the-art research results over a wide range of approaches from theory and concepts to real-world applications. As such, the volume will be very useful to researchers in applied mathematics, computational physics and mechanical engineering, as well as scientists working in coupled fluid flow models in biology or environmental applications.

Kambiz Vafai, Professor
University of California, Riverside
Department of Mechanical Enigineering
Riverside, California


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