9R48. Theory and Applications of Nonviscous Fluid Flows. - RK Zeytounian (Retired). Springer-Verlag, Berlin. 2002. 294 pp. ISBN 3-540-41412-6. $84.95.
Reviewed by J Crepeau (Dept of Mech. Eng., Univ of Idaho, 1776 Science Center Dr, Idaho Falls ID 83402).
There is no dearth of texts on inviscid flows, so any new contribution must distinguish itself from the pack. The author chooses to do this by presenting, in his view, a modern approach to key problems in nonviscous fluid flow. The book treats a variety of fluids applications from an applied mathematics as opposed to theoretical or high-level mathematical perspective. Much of the abstract nature and mathematical rigor of presenting hypotheses and proving theorems is avoided, and the focus is on the nuts and bolts of various techniques to solve problems.
The first three chapters are devoted to general fluid models and an overview of solution techniques. As a demonstration of the power of scaling, the author shows over what ranges of Knudsen number (ratio of the molecular mean free path to the length scale of the flow) the microscopic Boltzmann equations are applicable and where solutions to Euler’s equation apply. Then, a fairly standard continuum approach to Newtonian fluids and a derivation of the Navier-Stokes-Fourier equations are presented. The third chapter is a brief presentation/review of perturbation and asymptotic methods focusing on the method of matched asymptotic expansions and an efficient multiple-scale method over the method of strained coordinates. The strained coordinates approach is eschewed in favor of the others because of its poor performance in modeling partial differential equations.
Chapters 4–8 comprise the main applications portion of the text. The applications are broad-based and varied, including hydro- and aerodynamics problems, atmospheric flows, low Mach number flows and acoustics, turbomachinery flows, and shock layers. Within each application, many related topics are analyzed, providing an in-depth discussion and detailed theoretical treatment of the highlighted area. These chapters provide a thorough applied study of perturbation and asymptotic methods, and the details are well-presented. For those desiring a more rigorous mathematical analysis, the final chapter addresses these issues. It primarily focuses on the well-posedness of the governing equations and the existence and uniqueness of the solutions.
While the author touts a variety of modern theoretical analysis and modeling of inviscid flows, the primary and most prevalent tool employed is that of asymptotic analysis. Very little is done in the way of complex analysis or potential flow theory, which is odd for a text on nonviscous flows. Many symbolic manipulation programs can be used to evaluate asymptotic expansions, yet these methods are not addressed. There is no discussion of flows in microelectromechanical systems, which is tailored to a microscopic particle analysis, embodied in the fluid dynamics application of the Boltzmann equation and small length scales. There are few figures in the text, their quality ranges from fair to poor, and they lack a consistent format style and presentation, especially the line drawings.
Theory and Applications of Nonviscous Fluid Flows is more well-suited as a reference text rather than the primary classroom text, although it may serve as a complementary tome. There are no end-of-chapter homework problems or example problems, though one could argue that from Chapter 4 on, each section is a solution of a particular problem. It is written at an advanced graduate level; a previous course in perturbation methods is helpful in following the presentation, since the focus is on these techniques to solve the given problems.