The finite element method for fluid dynamics

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Bibliographic Details
Main Author Zienkiewicz, O. C.
Other Authors Taylor, Robert L. 1934-, Nithiarasu, Perumal
Format Electronic eBook
LanguageEnglish
Published Amsterdam ; Boston : Elsevier Butterworth-Heinemann, 2005.
Edition6th ed.
Subjects
Finite element method.
Mechanics, Applied.
Fluid dynamics.
elektronické knihy
electronic books
Online AccessPlný text

Cover

Table of Contents:
  • Cover
  • Contents
  • Preface
  • Acknowledgements
  • 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
  • 2 Convection dominated problems
  • finite element approximations to the convection-diffusion-reaction equation
  • 2.1 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
  • References
  • 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 Babu ka
  • 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
  • 4 Incompressible Newtonian laminar flows
  • 4.1 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
  • 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
  • 6 Free surface and buoyancy driven flows
  • 6.1 Introduction
  • 6.2 Free surface flows
  • 6.3 Buoyancy driven flows
  • 6.4 Concluding remarks
  • References
  • 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
  • tidtid6389

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