The finite element method for fluid dynamics
The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics.The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and...
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| Hlavní autoři: | , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Oxford ; Tokyo
Butterworth-Heinemann
2014
Elsevier Science & Technology |
| Vydání: | 7 |
| Témata: | |
| ISBN: | 1856176355, 9781856176354 |
| On-line přístup: | Získat plný text |
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- 3.9.3 Application of real boundary conditions in the discretization using the CBS algorithm -- 3.10 The performance of two- and single-step algorithms -- 3.11 Performance of dual time stepping to remove pressure error -- 3.12 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 -- 4.2.1 The fully explicit artificial compressibility form -- 4.2.2 The semi-implicit form -- 4.2.3 Quasi-implicit solution -- 4.3 Adaptive mesh refinement -- 4.3.1 Second gradient (curvature) based refinement -- 4.3.2 Local patch interpolation: Superconvergent values -- 4.3.3 Estimation of second derivatives at nodes -- 4.3.4 Element elongation -- 4.3.5 First derivative (gradient) based refinement -- 4.3.6 Choice of variables -- 4.3.7 An example -- 4.4 Adaptive mesh generation for transient problems -- 4.5 Slow flows: Mixed and penalty formulations -- 4.5.1 Analogy with incompressible elasticity -- 4.5.2 Mixed and penalty discretization -- 4.6 Concluding remarks -- References -- 5 Incompressible Non-Newtonian Flows -- 5.1 Introduction -- 5.2 Non-Newtonian flows: Metal and polymer forming -- 5.2.1 Non-Newtonian flows including viscoplasticity and plasticity -- 5.2.2 Steady-state problems of forming -- 5.2.3 Transient problems with changing boundaries -- 5.2.4 Elastic springback and viscoelastic fluids -- 5.3 Viscoelastic flows -- 5.3.1 Governing equations -- 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 -- 6.2.1 General remarks -- 6.2.1.1 Lagrangian methods -- 6.2.1.2 Eulerian methods -- 6.2.1.3 Arbitrary Langrangian-Eulerian (ALE) methods -- 6.2.2 Lagrangian method -- 6.2.3 Eulerian methods
- 6.2.3.1 Mesh updating or regeneration methods -- 6.2.3.2 Hydrostatic adjustment -- 6.2.3.3 Numerical examples using mesh regeneration methods -- 6.2.4 Arbitrary Langrangian-Eulerian (ALE) method -- 6.2.4.1 ALE implementation -- 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 -- 7.3.1 Euler equation -- 7.3.2 Navier-Stokes equations -- 7.4 Numerical approximations and the CBS algorithm -- 7.5 Shock capture -- 7.5.1 Second derivative-based methods -- 7.5.2 Residual-based methods -- 7.6 Variable smoothing -- 7.7 Some preliminary examples for the Euler equation -- 7.8 Adaptive refinement and shock capture in Euler problems -- 7.8.1 General -- 7.8.2 The h-refinement process and mesh enrichment -- 7.8.3 h-refinement and remeshing in steady-state two-dimensional problems -- 7.9 Three-dimensional inviscid examples in steady state -- 7.9.1 Solution of the flow pattern around a complete aircraft -- 7.9.2 THRUST: The supersonic car -- 7.10 Transient two- and three-dimensional problems -- 7.11 Viscous problems in two dimensions -- 7.11.1 Adaptive refinement in both shock and boundary layer -- 7.11.2 Special adaptive refinement for boundary layers and shocks -- 7.12 Three-dimensional viscous problems -- 7.13 Boundary layer: Inviscid Euler solution coupling -- 7.14 Concluding remarks -- References -- 8 Turbulent Flows -- 8.1 Introduction -- 8.1.1 Time averaging -- 8.1.2 Relation between κ, ε, and νT -- 8.2 Treatment of incompressible turbulent flows -- 8.2.1 Reynolds-averaged Navier-Stokes -- 8.2.2 One-equation models -- 8.2.2.1 Wolfstein κ-l model cite.wolfstein70[5] -- 8.2.2.2 Spalart-Allmaras (SA) model cite.spalart92[6] -- 8.2.3 Two-equation models -- 8.2.3.1 The standard κ-ε model
- Intro -- Half Title -- Author Biography -- Title Page -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- Preface -- 1 Introduction to the Equations of Fluid Dynamics and the Finite Element Approximation -- 1.1 General remarks and classification of fluid dynamics -- 1.2 The governing equations of fluid dynamics -- 1.2.1 Velocity, strain rates, and stresses in fluids -- 1.2.2 Constitutive relations for fluids -- 1.2.3 Mass conservation -- 1.2.4 Momentum conservation: Dynamic equilibrium -- 1.2.5 Energy conservation and equation of state -- 1.2.6 Boundary conditions -- 1.2.7 Navier-Stokes and Euler equations -- 1.3 Inviscid, incompressible flow -- 1.3.1 Velocity potential solution -- 1.4 Incompressible (or nearly incompressible) flows -- 1.5 Numerical solutions -- 1.5.1 Strong and weak forms -- 1.5.1.1 Weak form of equations -- 1.5.2 Weighted residual approximation -- 1.5.3 The Galerkin finite element method -- 1.5.4 A finite volume 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 -- 2.2.1 General remarks -- 2.2.2 Petrov-Galerkin methods for upwinding in one dimension -- 2.2.2.1 Continuity requirements for weighting functions -- 2.2.3 Balancing diffusion in one dimension -- 2.2.4 A variational principle in one dimension -- 2.2.5 Galerkin least-squares approximation (GLS) in one dimension -- 2.2.6 Subgrid scale (SGS) approximation -- 2.2.7 The finite increment calculus (FIC) for stabilizing the convective-diffusion equation in one dimension -- 2.2.8 Higher-order approximations -- 2.3 The steady-state problem in two (or three) dimensions -- 2.3.1 General remarks -- 2.3.2 Streamline (upwind) Petrov-Galerkin weighting (SUPG)
- 11.9 Infinite elements
- 8.2.4 Nondimensional form of the governing equations -- 8.2.4.1 κ-l model -- 8.2.4.2 Spalart-Allmaras model -- 8.2.4.3 κ-ε model -- 8.2.5 Shortest distance to a solid wall -- 8.2.6 Solution procedure for turbulent flow equations -- 8.3 Treatment of compressible flows -- 8.3.1 Mass-weighted (Favre) time averaging -- 8.4 Large eddy simulation (LES) -- 8.4.1.1 Standard SGS model -- 8.5 Detached eddy simulation and monotonically integrated LES -- 8.6 Direct numerical simulation (DNS) -- 8.7 Concluding remarks -- References -- 9 Generalized Flow and Heat Transfer in Porous Media -- 9.1 Introduction -- 9.2 A generalized porous medium flow approach -- 9.2.1 Nondimensional scales -- 9.3 Discretization procedure -- 9.3.1 Semi- and quasi-implicit forms -- 9.4 Forced convection -- 9.5 Natural convection -- 9.5.1 Constant-porosity medium -- 9.6 Concluding remarks -- References -- 10 Shallow-Water Problems -- 10.1 Introduction -- 10.2 The basis of the shallow-water equations -- 10.3 Numerical approximation -- 10.4 Examples of application -- 10.4.1 Transient one-dimensional problems: A performance assessment -- 10.4.2 Two-dimensional periodic tidal motions -- 10.4.3 Tsunami waves -- 10.4.4 Steady-state solutions -- 10.5 Drying areas -- 10.6 Shallow-water transport -- 10.7 Concluding remarks -- References -- 11 Long and Medium Waves -- 11.1 Introduction and equations -- 11.2 Waves in closed domains: Finite element models -- 11.3 Difficulties in modeling surface waves -- 11.4 Bed friction and other effects -- 11.5 The short-wave problem -- 11.6 Waves in unbounded domains (exterior surface wave problems) -- 11.6.1 Background to wave problems -- 11.6.2 Wave diffraction -- 11.6.3 Incident waves, domain integrals, and nodal values -- 11.7 Unbounded problems -- 11.8 Local nonreflecting boundary conditions (NRBCs) -- 11.8.1 Sponge layers or perfectly matched layers (PMLs)
- 2.3.3 Galerkin least squares (GLS) and finite increment calculus (FIC) in multidimensional problems -- 2.4 Steady state: Concluding remarks -- 2.5 Transients: Introductory remarks -- 2.5.1 Mathematical background -- 2.5.2 Possible discretization procedures -- 2.6 Characteristic-based methods -- 2.6.1 Mesh updating and interpolation methods -- 2.6.2 Characteristic-Galerkin procedures -- 2.6.3 A simple explicit characteristic-Galerkin procedure -- 2.6.4 Boundary conditions: Radiation -- 2.7 Taylor-Galerkin procedures for scalar variables -- 2.8 Steady-state condition -- 2.9 Nonlinear 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 Nondimensional form of the governing equations -- 3.3 Characteristic-based split (CBS) algorithm -- 3.3.1 The split: General remarks -- 3.3.2 The split: Temporal discretization -- 3.3.3 Spatial discretization and solution procedure -- 3.3.4 Mass diagonalization (lumping) -- 3.4 Explicit, semi-implicit, and nearly implicit forms -- 3.4.1 Fully explicit form -- 3.4.2 Semi-implicit form -- 3.4.3 Quasi- (nearly) implicit form -- 3.4.4 Evaluation of time step limits: Local and global time steps -- 3.5 Artificial compressibility and dual time stepping -- 3.5.1 Artificial compressibility for steady-state problems -- 3.5.2 Artificial compressibility in transient problems (dual time stepping) -- 3.6 ``Circumvention'' of the Babuška-Brezzi (BB) restrictions -- 3.7 A single-step version -- 3.8 Splitting error -- 3.8.1 Elimination of first-order pressure error -- 3.9 Boundary conditions -- 3.9.1 Fictitious boundaries -- 3.9.2 Real boundaries