1.

Record Nr.

UNINA9910458250703321

Autore

Zienkiewicz O. C. <1921-2009>

Titolo

The Finite Element Method Set [[electronic resource]]

Pubbl/distr/stampa

Burlington, : Elsevier Science, 2005

ISBN

1-282-38134-2

9786612381348

0-08-053167-9

Edizione

[6th ed.]

Descrizione fisica

1 online resource (457 p.)

Altri autori (Persone)

TaylorRobert L <1934-> (Robert Leroy)

Disciplina

515

620.10601515353

Soggetti

Mathematical analysis

Civil Engineering

Civil & Environmental Engineering

Engineering & Applied Sciences

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di contenuto

Front Cover; The Finite Element Method for Fluid Dynamics; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. Introduction to the equations of fluid dynamics and the finite element approximation; 1.1 General remarks and classification of fluid dynamics problems discussed in this book; 1.2 The governing equations of fluid dynamics; 1.3 Inviscid, incompressible flow; 1.4 Incompressible (or nearly incompressible) flows; 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation; 1.6 Concluding remarks; References

Chapter 2. Convection dominated problems- finite element approximations to the convection-diffusion-reaction equation2.1 Introduction; 2.2 The steady-state problem in one dimension; 2.3 The steady-state problem in two (or three) dimensions; 2.4 Steady state - concluding remarks; 2.5 Transients - introductory remarks; 2.6 Characteristic-based methods; 2.7 Taylor-Galerkin procedures for scalar variables; 2.8 Steady-state condition; 2.9 Non-linear waves and shocks; 2.10 Treatment of pure convection; 2.11 Boundary conditions



for convection-diffusion; 2.12 Summary and concluding remarks

ReferencesChapter 3. The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow; 3.1 Introduction; 3.2 Non-dimensional form of the governing equations; 3.3 Characteristic-based split (CBS) algorithm; 3.4 Explicit, semi-implicit and nearly implicit forms; 3.5 Artificial compressibility and dual time stepping; 3.6 'Circumvention' of the BabusĖŒka-Brezzi (BB) restrictions; 3.7 A single-step version; 3.8 Boundary conditions; 3.9 The performance of two-step and one-step algorithms on an inviscid problem; 3.10 Concluding remarks; References

Chapter 4. Incompressible Newtonian laminar flows4.1 Introduction and the basic equations; 4.2 Use of the CBS algorithm for incompressible flows; 4.3 Adaptive mesh refinement; 4.4 Adaptive mesh generation for transient problems; 4.5 Slow flows - mixed and penalty formulations; 4.6 Concluding remarks; References; Chapter 5. Incompressible non-Newtonian flows; 5.1 Introduction; 5.2 Non-Newtonian flows - metal and polymer forming; 5.3 Viscoelastic flows; 5.4 Direct displacement approach to transient metal forming; 5.5 Concluding remarks; References

Chapter 6. Free surface and buoyancy driven flows6.1 Introduction; 6.2 Free surface flows; 6.3 Buoyancy driven flows; 6.4 Concluding remarks; References; Chapter 7. Compressible high-speed gas flow; 7.1 Introduction; 7.2 The governing equations; 7.3 Boundary conditions - subsonic and supersonic flow; 7.4 Numerical approximations and the CBS algorithm; 7.5 Shock capture; 7.6 Variable smoothing; 7.7 Some preliminary examples for the Euler equation; 7.8 Adaptive refinement and shock capture in Euler problems; 7.9 Three-dimensional inviscid examples in steady state

7.10 Transient two- and three-dimensional problems

Sommario/riassunto

The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method