Asymptotic Analysis and Boundary Layers

ISBN-13: 9783642079832 / Angielski / Miękka / 2010 / 434 str.

Jean Cousteix;Jacques Mauss

Opis

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

Recenzje

From the book reviews:

"The book falls into two quite distinct parts, reflecting the expertises of the two authors. The first part gives a detailed and formal description of asymptotic methods, whilst the second part considers a number of fluid mechanics problems. ... There are numerous problems presented at the end of each chapter, which are accompanied by extremely comprehensive solutions ... . this book should prove a useful text for final year undergraduate students and for postgraduate (both taught and research) students wishing to master modern asymptotic methods." (P. W. Duck, Mathematical Reviews, Issue 2008 a)

"The novelty of this book lies in the use of thorough and advanced singular perturbation methods in combination with detailed applications to fluid mechanics. ... In the combination of asymptotics and fluid mechanics in such a fundamental and detailed approach, the book is unique in the science literature." (Ferdinand Verhulst, Dynamical Systems Magazine, October, 2007)

"Asymptotic Analysis and Boundary Layers is an extended English edition of Analyse asymptotique et couche limite published in the Springer series Mathématique et Applications. The book presents a new method of asymptotic analysis of boundary layer problems, the successive Complementary Expansion Method (SCEM). ... With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is selfcontained. It is accessible to graduate and postgraduate students of engineering and physics with a good knowledge in fluid mechanics." (Francisco Perez Acosta, Zentralblatt MATH, Vol. 1115 (17), 2007)

Spis treści

to Singular Perturbation Problems.- Boundary Layer Structure.- Asymptotic Expansions.- Successive Complementary Expansion Method.- Ordinary Differential Equations.- High Reynolds Number Flows.- Interactive Boundary Layer.- Applications of Interactive Boundary Layer Models.- Regular Forms of Interactive Boundary Layer.- Turbulent Boundary Layer.- Channel Flow.- Conclusion.

Blurb

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified.
With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will esteem it as a valuable monograph in their field of work.

Asymptotic Analysis and Boundary Layers is an extended English edition of Analyse asymptotique et couche limite published in the Springer series Mathématiques et Applications.