Stability and Wave Motion in Porous Media - (Applied Mathematical Sciences) by Brian Straughan (Hardcover)

About the Book

This book presents an account of theories of flow in porous media which have proved tractable to analysis and computation. In particular, the theories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail.

Book Synopsis

This book presents an account of theories of flow in porous media which have proved tractable to analysis and computation. In particular, the theories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, the theory of voids in an elastic material due to Cowin and Nunziato is discussed. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under consideration, and spatial stability are investigated. Applications to a variety of problems in porous media are included. This book is intended for graduate students and researchers in the mechanics, physics and engineering fields.

From the Back Cover

This book describes several tractable theories for fluid flow in porous media while the important mathematical questions about structural stability and spatial decay are addressed. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer.

Nonlinear wave motion in porous media is analysed, and waves in an elastic body with voids are investigated. Acoustic waves in porous media are also analysed in some detail.

A chapter is included on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media.

Brian Straughan is a professor at the Department of Mathematical Sciences at Durham University, United Kingdom.

Review Quotes

From the reviews:

"It offers an original approach to this multifaceted subject, not only because of the emphasis it puts on the stability issue, but also because of the exceptional variety of the problems addressed. ... this is a highly recommendable book. People having already some knowledge of flows in porous media will be delighted to read it, and beginners will find a valuable guide to understanding many challenging problems, treated with mathematical rigour, but never forgetting the physics." (Antonio Fasano, Mathematical Reviews, Issue 2009 e)

"It could be used in a seminar where graduate students are asked to research and present detailed arguments for select problems which are only formulated by Straughan or maybe only briefly outlined. As a research text, it surveys a great many interesting problems and applications ... with proper acknowledgment of and direction to the appropriate sources of the models and analysis. Thus, this text should be a valuable resource for anybody working on problems in the porous media field." (Philip W. Schaefer, SIAM Review, Vol. 54 (2), 2012)