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Principles of computational fluid dynamics. (English) Zbl 0960.76002
Springer Series in Computational Mathematics. 29. Berlin: Springer. xii, 644 p. (2000).
The book presents a vast area of numerical method used for the solution of fluid dynamics problems (the bibliography contains more than 450 titles). The book presents not only computational methods, but also describes theoretical principles necessary for the formulation of the corresponding mathematical problems. The first two chapters (of the 14 chapters of the volume) are just devoted to these theoretical principles of fluid dynamics, including constitutive, mechanical and thermodynamical theories. We mention only some of them: stationary and nonstationary convection-diffusion equations, compressible and incompressible Navier-Stokes equations, Euler equations in one- and multidimensional domains, the shallow water theory. Only celestial and oceanographic aspects are omitted, as the author remarks himself. The following 12 chapters are of purely computational character and describe finite volume and finite difference discretizations, iterative methods, discretization techniques in general domains, and scalar conservation laws. Specific problems analyzed in these chapters illustrate the general methods: the vertex-centered discretization, cell-centered discretization, upward discretization, non-uniform grids, defect correction, general stability of numerical methods and, in particular, strong stability, colocated and staggered grids, unified schemes and many other applications.
From this short presentation it is clear that this book written by a recognized expert in the field can be a useful tool to specialists and beginners, at the same time, in the computational fluid dynamics.

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Mxx Basic methods in fluid mechanics
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems