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Zbl 0991.74004
Zienkiewicz, O.C.; Taylor, R.L.
Finite element method. Vol. 3: Fluid dynamics. 5th ed. (English)
[B] Oxford: Butterworth-Heinemann. 352 p. \$ 40.00 (2000). ISBN 0-7506-5050-8/hbk; ISBN 0-7506-5160-1/3-vol.-set

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.
[L.P.Lebedev (Rostov-na-Donu)]

MSC 2000:: *74-02 Research monographs (mechanics of deformable solids)
76-02 Research monographs (fluid mechanics)
76M10 Finite element methods
65M60 Finite numerical methods (IVP of PDE)
65N30 Finite numerical methods (BVP of PDE)

Keywords: finite element method; characteristic-based split algorithm; incompressible fluid; compressible fluid; buoyancy driven flows; turbulence; discretization; error estimate; Navier-Stokes equations; shallow water waves

Citations: Zbl 0991.74005; Zbl 0991.74006

Cited in: Zbl 1084.74001

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