5R48. Fluid Dynamics: Theory, Computation, and Numerical Simulation. - C Pozrikidis (Dept of Appl Mech and Eng Sci, Univ of California, La Jolla CA 92093-0411). Kluwer Acad Publ, Norwell MA. 2001. 675 pp. ISBN 0-7923-7351-0. $140.00.

Reviewed by DK Gartling (Comp Fluid Dyn, Sandia Natl Labs, MS 0826, Albuquerque NM 87185-5800).

There are a wide variety of undergraduate fluid dynamics texts available, and all claim to have some unique attribute that makes them the better choice for the classroom. The aim of the present book is to merge the study and use of numerical methods with the theory and solutions of classical fluid dynamics. The idea is quite reasonable given that so much of current engineering flow analysis is based on computer simulation. However, it is not clear that a combination of two very extensive subjects can be adequately addressed in a single text. This book has a very thorough treatment of isothermal, low speed fluid dynamics at the undergraduate level. The topics on numerical methods are considered in a much more superficial manner though, in many cases, they are integrated nicely with the fluid dynamics applications. The text is coupled to a software library that can be downloaded and run on modest hardware. This is a very appealing feature in that it permits the student to conveniently evaluate and study a variety of flow problems and hopefully gain a better physical feeling for fluid dynamics.

The first two chapters are extensive and cover all of the standard topics associated with fluid kinematics including coordinate systems, deformations, streamlines, streaklines and particle paths, vector analysis, material derivatives, mass conservation, and the continuity equation. Numerical techniques for simple ordinary differential equations, interpolation, and numerical differentiation are introduced as part of the solution methods for problems in kinematics. Chapter 3 continues with irrotational flows and the formulation and solution of potential problems. Point singularities and distributions for the potential field are discussed, and the finite difference method for Laplace’s equation is introduced. Sections on derivative approximations, linear algebraic equations, boundary condition imposition, and matrix solvers are included among the numerical topics.

Chapter 4 introduces forces and stresses and the ideas of viscosity and constitutive relations for Newtonian and non-Newtonian fluids. The next chapter considers problems in hydrostatics including forces on submerged objects and a variety of free surface and contact angle problems. The numerical methods described in conjunction with these problems include Newton’s method for a single equation and shooting methods for ordinary differential equations. Chapter 6 returns to purely fluid mechanics topics and is concerned with the equations of motion in both differential and integral form. Boundary conditions are described, and there are sections on the Euler and Navier-Stokes equations as well as the vorticity transport equation. The seventh chapter is quite lengthy and provides a very complete catalog of analytic and semi-analytic solutions for tube and channel flows and simple flows next to walls. The computer work associated with this chapter is primarily the evaluation of complex solutions with variations in geometric and flow parameters.

The finite difference method for incompressible, viscous flows is the main subject of Chapter 8. Initially, difference methods are introduced for the solution of simplified flow equations. The second part of the chapter considers primitive variable and vorticity transport formulations for the two-dimensional driven cavity problem. Though the illustrations and graphics throughout the text are generally good, the velocity vector plots in this chapter are not very helpful. The next two chapters consider flows at the extremes in Reynolds number. The low Reynolds number chapter discusses all of the standard lubrication flows, film flows, corner flows, and point source methods and also introduces the finite volume method. The high Reynolds number chapter covers the classic boundary layer methods and flow stability, and introduces turbulence and mathematical descriptions of turbulence. Vortex motions in the absence of viscosity form the subject of Chapter 11 with sections on point vortices, contour dynamics, and the Biot-Savart integral. The last chapter deals with panel methods for external inviscid flows. The numerical work for these last few chapters mostly involves the application of methods described in previous chapters. The book concludes with an appendix describing the contents of the available software library and a marginally adequate index.

As an undergraduate text on fluid dynamics, this is a very complete and well-written book. The numerical methods featured in the book are elementary, but are worthwhile in the context of undergraduate study. The software available with the book is also a useful adjunct for study. Fluid Dynamics: Theory, Computation, and Numerical Simulation is certainly recommended for consideration as a classroom text. Those with an interest in fluid mechanics at the graduate or post-graduate level might find the book a useful reference; those seeking a treatise on numerical methods or computational fluid dynamics will find the text of limited value.