Foreword

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.