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Kinetic Theory and Fluid Dynamics [Hardcover]

Yoshio Sone

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Book Description

October 4, 2002 0817642846 978-0817642846 2002

This monograph gives a comprehensive description of the relationship and connections between kinetic theory and fluid dynamics, mainly for a time-independent problem in a general domain. Ambiguities in this relationship are clarified, and the incompleteness of classical fluid dynamics in describing the behavior of a gas in the continuum limit—recently reported as the ghost effect—is also discussed. The approach used in this work engages an audience of theoretical physicists, applied mathematicians, and engineers.

By a systematic asymptotic analysis, fluid-dynamic-type equations and their associated boundary conditions that take into account the weak effect of gas rarefaction are derived from the Boltzmann system. Comprehensive information on the Knudsen-layer correction is also obtained. Equations and boundary conditions are carefully classified depending on the physical context of problems. Applications are presented to various physically interesting phenomena, including flows induced by temperature fields, evaporation and condensation problems, examples of the ghost effect, and bifurcation of flows.

Kinetic Theory and Fluid Dynamics serves as a bridge for those working in different communities where kinetic theory is important: graduate students, researchers and practitioners in theoretical physics, applied mathematics, and various branches of engineering.

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Editorial Reviews


"Yoshio Sone is certainly one of the world leading experts for continuum limits of the Boltzmann equation and with this book he summarizes the extensive work of his group on this subject. The text is very carefully written and even if the expansions and equations are lengthy, the results are always interpreted and discussed. ... Altogether, the book is a rich source on the theory of kinetic boundary layers in the continuum limit and it is certainly valuable for those working in fields where kinetic theory or fluid dynamics is important."  —ZAMP

"This book gives an impressive overview of the formidable amount of work done by the author . . . [It] is very detailed, and very carefully written, aimed at a great generality of results and physical situations . . . Interesting physical phenomena and engineering applications are presented throughout . . . supported by numerical analysis and sometimes even by experimental demonstration. All of that makes the book appealing in various fields, including applied mathematics, physics, and engineering, especially at the level of graduate students and young researchers."   —European Journal of Mechanics, B/Fluids

"This book will be a useful and lasting reference point for kinetic boundary layers in the continuum limit. It isn't reading for the faint at heart—the technical skill and fearlessness of lengthy expansions of the author are visible. Yet this is a collection of a lifetime of research, conveniently collected in one place."   —Mathematical Reviews

"This is a comprehensive study on the relationship between…classical (continuum) fluid dynamics and…kinetic theory. In particular, the incompleteness of classical fluid dynamics in describing the time evolution of real gases is also discussed.

The fluid dynamics equations are derived by the methods of asymptotic analysis from the Boltzmann system. All equations resulting from this process are classified with respect to their physical context. Applications are given in order to illustrate various interesting physical phenomena: the flows induced by temperature fields, evaporation and condensation problems, examples of the so-called ghost effect, and bifurcations of flows.

In general, many applications are discussed without a sophisticated mathematical apparatus not easily accessible to engineers. On the other hand, experimental work is examined to supplement the theory, and mathematicians will certainly benefit from [the] clarity of definitions and precise physical description[s].… The book is intended for theoretical physicists, applied mathematicians, engineers, and students in mathematics."   —Applications of Mathematics

"The book written by Sone is in many respects excellent. It is very well structured, e.g. most chapters start with the definition of a problem, followed by the method of solution, a summary of the results and finally a number of applications. The calculations and interpretations are extremely accurate and reliable. The book makes an impression of completeness in the sense that the topics treated are presented in an exhaustive manner and the references are abundant… The book is no doubt an acquisition to the literature in the field of Kinetic Theory and Fluid Dynamics. It will prove to be an important tool for many graduate students and researchers in Applied, Mathematics, Physics and, since it also contains many engineering applications, Mechanical Engineering."   —Physica B

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