9R39. Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations. Cambridge Texts in Applied Mathematics. - C Cercignani (Dept of Math, Politechnic Univ, Milan, Italy). Cambridge UP, Cambridge, UK. 2000. 320 pp. Softcover. ISBN 0-521-65992-2 $29.95.

Reviewed by C Michaelis (Appl Phys Lab, Mission Concept and Anal Group, Johns Hopkins Univ, 11100 Johns Hopkins Rd, Laurel MD 20723-6099).

Cercignani’s latest book delves into a broad and mostly theoretical overview of rarefied flows. The aim of the book is to present the concepts, methods, and applications of kinetic theory to rarefied gas dynamics. The book begins with a discussion of fundamentals, including the derivation of the Boltzmann model and the development of various approximations based principally on the BGK model. Following this introduction, several model problems are introduced to aid in understanding the basic concepts in what is otherwise a very complex and difficult topic. To accomplish this, the author presents several variations of the classic one-dimensional Couette flow problem which are mathematically simple enough for a theoretical treatment. Perturbation methods and numerical computations are used to further the development and to gain insight.

Following a discussion of the simple one-dimensional problem, the focus turns to flows with multiple dimensions. Specifically, perturbation methods are used to study the linearized, steady Boltzmann equation. The resulting models are studied in both the continuum, free molecular, and nearly free molecular flow regimes to further illustrate the concepts of rarefied gas dynamics. The author then moves on to a brief discussion of gas mixtures and polyatomic gases where internal energies and chemical reactions are important. The book excludes any discussion of ionized and radiating flows. The theoretical development in the book concludes with a detailed discussion of condensation and evaporation phenomena in rarefied flows, including a development of appropriate boundary conditions for the Boltzmann equation. Once again, a simple one-dimensional parallel plate (Couette) model is used to emphasize the basic concepts.

In addition to the numerous theoretical discussions, this book includes a detailed introduction to numerical solutions of rarefied flows along with a few representative solutions. Cercignani introduces the reader to the Direct Simulation Monte Carlo method developed by GA Bird in the early 1960s. This engineering method is the most widely used for rarefied flows. Often omitted from many classic texts in the field, the discussion of numerical methods compliments well the vast theory that is otherwise the focus of the book.

The author’s expertise in kinetic theory is unrivaled and certainly evident in the work. The author has written several other books on rarefied flows, including The Mathematical Theory of Dilute Gases, Mathematical Methods in Kinetic Theory, and The Boltzmann Equation and Its Applications. Stylistically speaking, the book reads well, despite the heavy emphasis on mathematics and theory. The figures and tables are generally concise and informative. One complaint is that in a few figures, the plotted variables were not well defined.

However, the book falls short of its aim to emphasize methods and applications. With the exception of the chapter on numerical methods, the author primarily focuses on theoretical discussions and academic problems that are generally geared toward graduate classes in applied mathematics and physics. Practicing engineers and graduate students in related engineering fields will probably find the book to be too mathematical to be helpful. For engineering students new to the field of rarefied gas dynamics, other classic texts, such as Physical Gas Dynamics by Vincenti and Kruger, will provide a better introduction to the study of rarefied flows. However, for engineers and scientists with a moderate level of prior expertise in the field, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations, is a great comprehensive reference that is certainly worth the low cost.