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Finite element method. Vol. 3: Fluid dynamics. 5th ed. (English) Zbl 0991.74004
Oxford: Butterworth-Heinemann. 352 p. $ 40.00 (2000).
This volume appears for the first time as a separate book in the fundamental treatment by Zienkiewicz and Taylor of problems of fluid mechanics using FEM. It is entirely independent of the previous two volumes [see the foregoing entries]. The book considers the mechanics of compressible and incompressible fluids and gases, turbulence, buoyancy driven flows, and traditional problems of shallow water waves. The main point, as in the whole book, is the implementation of workable algorithms based on FEM, and the evaluation of their accuracy and applicability. The main solution method is a characteristic-based split algorithm proposed by the authors. All steps of problem solutions, as well as the final results obtained, are explained with brilliant clarity. This volume is recommended to practical engineers in fluid dynamics as well as to researchers in the area. Mathematicians can find a large number of open problems on the convergence of FEM for many practical situations.

MSC:
74-02Research monographs (mechanics of deformable solids)
76-02Research monographs (fluid mechanics)
76M10Finite element methods (fluid mechanics)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)