Stability and Wave Motion in Porous Media

ISBN-13: 9781441926265 / Angielski / Miękka / 2010 / 439 str.

Brian Straughan

Opis

This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. 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 cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.

Recenzje

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)

Spis treści

Structural Stability.- Spatial Decay.- Convection in Porous Media.- Stability of Other Porous Flows.- Fluid - Porous Interface Problems.- Elastic Materials with Voids.- Poroacoustic Waves.- Numerical Solution of Eigenvalue Problems.

Blurb

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.