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.
Erscheinungsdatum: 12.08.2008

Straughan, B. (Brian)

New York: Springer

Springer US

Copernicus

Telos

Applied mathematical sciences -- v. 165, Applied mathematical sciences (Springer-Verlag New York Inc.) -- v. 165., New York, New York State, 2008

Applied mathematical sciences (Springer-Verlag New York Inc.), New York, c2008

United States, United States of America

165, 1. ed, New York, NY, 2008

Volume 165, 2008

Cut-off text on some pages due to text runs into the gutter

Includes bibliographical references (p. [399]-431) and index.

"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."--Jacket

xiv, 437 p. : 25 cm
Includes bibliographical references (p. [399]-431) and index
Introduction -- 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

Introduction -- 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. Brian Straughan. Includes Bibliographical References (p. [399]-431) And Index.

2023-06-28