Zienkiewicz O.C., Taylor L.R. The Finite Element Method. Volume 3: Fluid Dynamics

5th Edition. — Butterworth-Heinemann, 2000. — 348 p.Fifth edition, Taylor R.L. (на английском языке)
Классический учебник по газодинамике. Представлены основные методы, алгоритмы и программы решения задач по газовой динамикеIn the years since the fourth edition of this seminal work was published, active research has developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. Written by the pre-eminent professors in their fields, this new edition of the Finite Element Method maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. Expanded to three volumes the book now covers the basis of the method and its application to advanced solid mechanics and also advanced fluid dynamics. Volume Three: Fluid Dynamics is intended for readers studying fluid mechanics at a higher level. Although it is an ideal companion volume to Volume One: The Basis, this advanced text also functions as a "stand-alone" volume, accessible to those who have been introduced to the Finite Element Method through a different routePreface to Volume 3
AcknowledgementsIntroduction and the equations of fluid dynamics
General remarks and classification of fluid mechanics problems discussed in the book
The governing equations of fluid dynamics
Incompressible (or nearly incompressible) flows
Concluding remarks
Convection dominated problems - finite element appriximations to the convection-diffusion equationthe steady-state problem in one dimension
The steady-state problem in two (or three) dimensions
Steady state - concluding remarks
Transients - introductory remarks
Characteristic-based methods
Taylor-Galerkin procedures for scalar variables
Steady-state condition
Non-linear waves and shocks
Vector-valued variables
Summary and concludingA general algorithm for compressible and incompressible flows - the characteristic-based split (CBS) algorithmCharacteristic-based split (CBS) algorithm
Explicit, semi-implicit and nearly implicit forms
’Circumventing’ the Babuska-Brezzi (BB) restrictions
A single-step version
Boundary conditions
The performance of two- and single-step algorithms on an inviscid problems
Concluding remarksIncompressible laminar flow - newtonian and non-newtonian fluids
Introduction and the basic equations
Inviscid, incompressible flow (potential flow)
Use of the CBS algorithm for incompressible or nearly incompressible flows
Boundary-exit conditions
Adaptive mesh refinement
Adaptive mesh generation for transient problems
mportance of stabilizing convective terms
Slow flows - mixed and penalty formulations
Non-newtonian flows - metal and polymer forming
Direct displacement approach to transient metal forming
Concluding remarksFree surfaces, buoyancy and turbulent incompressible flowsFree surface flows
Buoyancy driven flows
Turbulent flowsCompressible high-speed gas flowThe governing equations
Boundary conditions - subsonic and supersonic flow
Numerical approximations and the CBS algorithm
Shock capture
Some preliminary examples for the Euler equation
Adaptive refinement and shock capture in Euler problems
Three-dimensional inviscid examples in steady state
Transient two and three-dimensional problems
Viscous problems in two dimensions
Three-dimensional viscous problems
Boundary layer-inviscid Euler solution coupling
Concluding remarksShallow-water problemsThe basis of the shallow-water equations
Numerical approximation
Examples of application
Drying areas
Shallow-water transport
Waves
Introduction and equations
Waves in closed domains - finite element models
Difficulties in modelling surface waves
Bed friction and other effects
The short-wave problem
Waves in unbounded domains (exterior surface wave problems)
Unbounded problems
Boundary dampers
Linking to exterior solutions
Infinite elements
Mapped periodic infinite elements
Ellipsoidal type infinite elements of Burnnet and Holford
Wave envelope infinite elements
Accuracy of infinite elements
Transient problems
Three-dimensional effects in surface wavesComputer implementation of the CBS algorithmThe data input module
Solution module
Output module
Possible extensions to CBSflow
Appendix A Non-conservative form of
Navier-Stokes equations
Appendix B Discontinuous Galerkin methods in
the solution of the convection-diffusion equation
Appendix C Edge-based finite element forumlation
Appendix D Multigrid methods
Appendix E Boundary layer-inviscid flow coupling
Author index
Subject index