كتاب Finite Element Method Volume 3 - Fluid Dynamics

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Finite Element Method Volume 3 - Fluid Dynamics

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1 Introduction and the equations of fluid dynamics
1.4 Concluding remarks
General remarks and classification of fluid mechanics problems
discussed in this book
The governing equations of fluid dynamics
Incompressible (or nearly incompressible) flows
References
2 Convection dominated problems - finite element approximations to the
convection-diffusion 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
2.8 Steady-state condition
2.9 Non-linear waves and shocks
2.10 Vector-valued variables
2.11 Summary and concluding remarks
Taylor-Galerkin procedures for scalar variables
References
3 A general algorithm for compressible and incompressible flows - the
characteristic-based split (CBS) algorithm
3.1 Introduction
3.2 Characteristic-based split (CBS) algorithm
3.5 A single-step version
3.6 Boundary conditions
Explicit, semi-implicit and nearly implicit forms
‘Circumventing’ the BabuSka-Brezzi (BB) restrictions
3.7 The performance of two- and single-step algorithms on an inviscid
problem 85
3.8 Concluding remarks 87
References 87
4 Incompressible laminar flow - newtonian and non-newtonian fluids 91
4.1 Introduction and the basic equations 91
4.2 Inviscid, incompressible flow (potential flow) 93
Use of the CBS algorithm for incompressible or nearly incompressible flows
Boundary-exit conditions
Adaptive mesh refinement
Adaptive mesh generation for transient problems
Importance 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 remarks
References
5 Free surfaces, buoyancy and turbulent incompressible flows
5.1 Introduction
5.2 Free surface flows
5.3 Buoyancy driven flows
5.4 Turbulent flows
References
6 Compressible high-speed gas flow
Introduction
The 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 remarks
References
7 Shallow-water problems
7.1 Introduction
7.3 Numerical approximation
The basis of the shallow-water equations
7.4 Examples of application
7.5 Drying areas
7.6 Shallow-water transport
References
8 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 Burnett and Holford
Wave envelope infinite elements
Accuracy of infinite elements
Transient problems
Three-dimensional effects in surface waves
References
9 Computer implementation of the CBS algorithm
9.1 Introduction
9.2 The data input module
9.3 Solution module
9.4 Output module
9.5 Possible extensions to CBSflow
References
Appendix A: Non-conservative form of Navier-Stokes equations
Appendix B: Discontinuous Galerkin methods in the solution of the
Appendix C: Edge-based finite element formulation
Appendix D: Multigrid methods
Appendix E: Boundary layer-inviscid flow coupling
Author index
Subject index
Volume 1: The basis
1. Some preliminaries: the standard discrete system
2. A direct approach to problems in elasticity
3. Generalization of the finite element concepts. Galerkin-weighted residual and
4. Plane stress and plane strain
5. Axisymmetric stress analysis
6. Three-dimensional stress analysis
7. Steady-state field problems - heat conduction, electric and magnetic potential,
8. ‘Standard’ and ‘hierarchical’ element shape functions: some general families of
9. Mapped elements and numerical integration - ‘infinite’ and ‘singularity’ elements
variational approaches
fluid flow, etc
Co continuity
10. The patch test, reduced integration, and non-conforming elements
1 1. Mixed formulation and constraints - complete field methods
12. Incompressible problems, mixed methods and other procedures of solution
13. Mixed formulation and constraints - incomplete (hybrid) field methods, bound-
14. Errors, recovery processes and error estimates
15. Adaptive finite element refinement
16. Point-based approximations; element-free Galerkin - and other meshless methods
17. The time dimension - semi-discretization of field and dynamic problems and
18. The time dimension - discrete approximation in time
19. Coupled systems
20. Computer procedures for finite element analysis
Appendix A. Matrix algebra
Appendix B. Tensor-indicia1 notation in the approximation of elasticity problems
Appendix C. Basic equations of displacement analysis
Appendix D. Some integration formulae for a triangle
Appendix E. Some integration formulae for a tetrahedron
Appendix F. Some vector algebra
Appendix G. Integration by parts
Appendix H. Solutions exact at nodes
Appendix I. Matrix diagonalization or lumping
ary/Trefftz methods
analytical solution procedures
Volume 2: Solid and structural mechanics
1. General problems in solid mechanics and non-linearity
2. Solution of non-linear algebraic equations
3. Inelastic materials
4. Plate bending approximation: thin (Kirchhoff) plates and C, continuity require-
5. ‘Thick’ Reissner-Mindlin plates - irreducible and mixed formulations
6. Shells as an assembly of flat elements
7. Axisymmetric shells
8. Shells as a special case of three-dimensional analysis - Reissner-Mindlin
9. Semi-analytical finite element processes - use of orthogonal functions and ‘finite
ments
assumptions
strip’ methods
10. Geometrically non-linear problems - finite deformation
1 1. Non-linear structural problems - large displacement and instability
12. Pseudo-rigid and rigid-flexible bodies
13. Computer procedures for finite element analysis
Appendix A: Invariants of second-order tensors

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كتاب Finite Element Method Volume 3 - Fluid Dynamics 761752

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