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Computational methods for fluid dynamics. 3rd rev. ed. (English) Zbl 0998.76001
Berlin: Springer. xiv, 423 p. (2002).
[For the 2nd ed. see Zbl 0943.76001.]
Until p. 36, there is a general discussion of partial differential equations encountered in CFD and methods for their solution. Then, chapter 3 contains a detailed presentation of finite difference methods, and chapter 4 gives a detailed discussion of finite volume method, the preferred method of the authors and the main topic of the book (FEM is not treated). Chapter 5 describes the whole spectrum of solution methods for linear systems of equations (direct and iterative), and also of nonlinear systems. Chapter 6 discusses methods for initial value problems (explicit and implicit methods, Runge Kutta methods). In chapter 7, the authors discuss the solution of Navier-Stokes equations with many “tricks” (non-staggered and staggered grids, coupled and uncoupled solutions, treatment of pressure). Chapter 8 examines different types of grids and related questions, and a discussion of turbulent flows (DNS, LES, Reynolds-averaged flows with different turbulence models) follows in chapter 9. Chapter 10 on compressible flows is rather a mere survey. In chapter 11 “Efficiency and accuracy improvement” a mix of problems is discussed: error analysis, grid quality, multigrid, grid refinement, parallel computing. Chapter 12 treats some special topics, e.g. moving grids and free surface flows. Finally, a list of Fortran 77 computer codes of the authors is given that is accessible in the Internet.
It is impossible to treat in detail all the subjects of the book on 423 pages. In reviewer’s opinion, the book is a mixture of surveys and detailed discussions, the latter reflecting the experience of the authors. Thus the book is valuable for the beginners and also for the specialists.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
65F05 Direct numerical methods for linear systems and matrix inversion
65F10 Iterative numerical methods for linear systems
76F65 Direct numerical and large eddy simulation of turbulence
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