5R1. Computational Aerodynamics and Fluid Dynamics: An Introduction. - J-J Chattot (Dept of Mech and Aeronaut Eng, Univ of California, 1 Shields Ave, Davis CA 95616). Springer-Verlag, Berlin. 2002. 186 pp. ISBN 3-540-43494-1. $54.95.
Reviewed by Shi Tsan Wu (Dept of Mech and Aerospace Eng, Univ of Alabama, Sparkman Dr, Huntsville AL 35899).
In this book, the author has documented his lecture notes on computational fluid dynamics (CFD) which he has developed over the past 20 years to form this textbook. This textbook is intended for senior undergraduate and first-year graduate students who will be developing or using codes in the numerical simulation of fluid flows or other physical phenomena governed by partial differential equations. The book is organized into 11 chapters. The fundamental numerical methods discussed in this book are based on the finite difference method as a method of discretization on Cartesian mesh systems, in the physical domain, or in the computational domain after coordinate transformation. The author has discussed the finite volume method for discretization for arbitrary mesh systems including unstructured meshes.
The fundamental theory and techniques are presented in Chapter 2, which include the Taylor expansion and the complex mode analysis. Further, the accuracy and stability analyses for these methods are also discussed.
The ordinary differential equations (ODEs) and their integration are given in Chapter 3. The general discussions of PDEs are given in Chapter 4, which include the discussions on the type and classifications of PDEs and the concepts of characteristic surfaces, computational relations, and the jump conditions associated with conservation laws. The connection between the physical phenomena of wave propagation, diffusion and equilibrium, and their mathematical counterparts are discussed well.
Chapters 5–7 discuss the linear model equations of hyperbolic, parabolic, and elliptic, respectively. Classical schemes such as centered scheme, upwind scheme, the Lax scheme, the Lax-Wendroff scheme, etc, are reviewed and discussed in terms of accuracy and stability. Practical aspects of the implementation of the selected schemes are presented.
Chapter 8 gives a specific discussion on the finite difference scheme for a convection-diffusion equation which includes the FTCS method, the Box and modified Box method, and a mixed type scheme.
Chapter 9 presents an excellent discussion on the method of Murman and Cole with a model problem of the 2D steady compressible flow past a body.
The author moves to the discussion of nonlinearities in Chapter 10. The explicit and implicit mixed-type schemes are given. Finally, the application to a system of equations for gasdynamics is discussed.
The most significant aspect of this book is that the author presents two appendices that include the problems and solutions, respectively.
In summary, Computational Aerodynamics and Fluid Dynamics: An Introduction is a very well-written book. This reviewer recommends it highly for advanced undergraduate and first-year graduate classes. In addition, engineers and scientists interested in numerical simulation of fluid flow and plasma flow should find this an excellent self-study textbook.