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Chung T.J. Computational Fluid Dynamics

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Chung T.J. Computational Fluid Dynamics
Second edition. — Cambridge University Press, 2010. — 1058 p. — ISBN: 978-0-521-76969-3 (Hardback).
The second edition of Computational Fluid Dynamics represents a significant improvement from the first edition. However, the original idea of including all computational fluid dynamics methods (FDM, FEM, FVM); all mesh generation schemes; and physical applications to turbulence, combustion, acoustics, radiative heat transfer, multiphase flow, electromagnetic flow, and general relativity is still maintained. This unique approach sets this book apart from its competitors and allows the instructor to adopt this book as a text and choose only those subject areas of his or her interest. The second edition includes a new section on preconditioning for EBE-GMRES and a complete revision of the section on flowfield-dependent variation methods, which demonstrates more detailed computational processes and includes additional example problems. For those instructors desiring a textbook that contains homework assignments, a variety of problems for FDM, FEM, and FVM are included in an appendix. To facilitate students and practitioners intending to develop a large-scale computer code, an example of FORTRAN code capable of solving compressible, incompressible, viscous, inviscid, 1D, 2D, and 3D for all speed regimes using the flowfield-dependent variation method is made available.
Contents
Preface to the First Edition page
Preface to the Revised Second Edition
Preliminaries
Introduction
General
Historical Background
Organization of Text
One-Dimensional Computations by Finite Difference Methods
One-Dimensional Computations by Finite Element Methods
One-Dimensional Computations by Finite Volume Methods
FVM via FDM
FVM via FEM
Neumann Boundary Conditions
FDM
FEM
FVM via FDM
FVM via FEM
Example Problems
Dirichlet Boundary Conditions
Neumann Boundary Conditions
Summary
References
Governing Equations
Classification of Partial Differential Equations
Navier-Stokes System of Equations
Boundary Conditions
Summary
References
Finite Difference Methods
Derivation of Finite Difference Equations
Simple Methods
General Methods
Higher Order Derivatives
Multidimensional Finite Difference Formulas
Mixed Derivatives
Nonuniform Mesh
Higher Order Accuracy Schemes
Accuracy of Finite Difference Solutions
Summary
References
Solution Methods of Finite Difference Equations
Elliptic Equations
Finite Difference Formulations
Iterative Solution Methods
Direct Method with Gaussian Elimination
Parabolic Equations
Explicit Schemes and von Neumann Stability Analysis
Implicit Schemes
Alternating Direction Implicit (ADI) Schemes
Approximate Factorization
Fractional Step Methods
Three Dimensions
Direct Method with Tridiagonal Matrix Algorithm
Hyperbolic Equations
Explicit Schemes and Von Neumann Stability Analysis
Implicit Schemes
Multistep (Splitting, Predictor-Corrector) Methods
Nonlinear Problems
Second Order One-Dimensional Wave Equations
Burgers’ Equation
Explicit and Implicit Schemes
Runge-Kutta Method
Algebraic Equation Solvers and Sources of Errors
Solution Methods
Evaluation of Sources of Errors
Coordinate Transformation for Arbitrary Geometries
Determination of Jacobians and Transformed Equations
Application of Neumann Boundary Conditions
Solution by MacCormack Method
Example Problems
Elliptic Equation (Heat Conduction)
Parabolic Equation (Couette Flow)
Hyperbolic Equation (First Order Wave Equation)
Hyperbolic Equation (Second Order Wave Equation)
Nonlinear Wave Equation
Summary
References
Incompressible Viscous Flows via Finite Difference Methods
General
Artificial Compressibility Method
Pressure Correction Methods
Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
Pressure Implicit with Splitting of Operators
Marker-and-Cell (MAC) Method
Vortex Methods
Summary
References
Compressible Flows via Finite Difference Methods
Potential Equation
Governing Equations
Subsonic Potential Flows
Transonic Potential Flows
Euler Equations
Mathematical Properties of Euler Equations
Quasilinearization of Euler Equations
Eigenvalues and Compatibility Relations
Characteristic Variables
Central Schemes with Combined Space-Time Discretization
Lax-Friedrichs First Order Scheme
Lax-Wendroff Second Order Scheme
Lax-Wendroff Method with Artificial Viscosity
Explicit MacCormack Method
Central Schemes with Independent Space-Time Discretization
First Order Upwind Schemes
Flux Vector Splitting Method
Godunov Methods
Second Order Upwind Schemes with Low Resolution
Second Order Upwind Schemes with High Resolution (TVD Schemes)
Essentially Nonoscillatory Scheme
Flux-Corrected Transport Schemes
Navier-Stokes System of Equations
Explicit Schemes
Implicit Schemes
PISO Scheme for Compressible Flows
Preconditioning Process for Compressible and Incompressible Flows
General
Preconditioning Matrix
Flowfield-Dependent Variation Methods
Basic Theory
Flowfield-Dependent Variation Parameters
FDV Equations
Interpretation of Flowfield-Dependent Variation Parameters
Shock-Capturing Mechanism
Transitions and Interactions between Compressible and Incompressible Flows Transitions and Interactions between Laminar and Turbulent Flows
Other Methods
Artificial Viscosity Flux Limiters
Fully Implicit High Order Accurate Schemes
Point Implicit Methods
Boundary Conditions
Euler Equations
One-Dimensional Boundary Conditions
Multi-Dimensional Boundary Conditions
Nonreflecting Boundary Conditions
Navier-Stokes System of Equations
Example Problems
Solution of Euler Equations
Triple Shock Wave Boundary Layer Interactions Using FDV Theory
Summary
References
Finite Volume Methods via Finite Difference Methods
General
Two-Dimensional Problems
Node-Centered Control Volume
Cell-Centered Control Volume
Cell-Centered Average Scheme
Three-Dimensional Problems
D Geometry Data Structure
Three-Dimensional FVM Equations
FVM-FDV Formulation
Example Problems
Summary
References
Finite Element Methods
Introduction to Finite Element Methods
General
Finite Element Formulations
Definitions of Errors
Summary
References
Finite Element Interpolation Functions
General
One-Dimensional Elements
Conventional Elements
Lagrange Polynomial Elements
Hermite Polynomial Elements
Two-Dimensional Elements
Triangular Elements Rectangular Elements
Quadrilateral Isoparametric Elements
Three-Dimensional Elements
Tetrahedral Elements
Triangular Prism Elements
Hexahedral Isoparametric Elements
Axisymmetric Ring Elements
Lagrange and Hermite Families and Convergence Criteria
Summary
References
Linear Problems
Steady-State Problems – Standard Galerkin Methods
Two-Dimensional Elliptic Equations
Boundary Conditions in Two Dimensions
Solution Procedure
Stokes Flow Problems
Transient Problems – Generalized Galerkin Methods
Parabolic Equations
Hyperbolic Equations
Multivariable Problems
Axisymmetric Transient Heat Conduction
Solutions of Finite Element Equations
Conjugate Gradient Methods (CGM)
Element-by-Element (EBE) Solutions of FEM Equations
Example Problems
Solution of Poisson Equation with Isoparametric Elements
Parabolic Partial Differential Equation in Two Dimensions
Summary
References
Nonlinear Problems/Convection-Dominated Flows
Boundary and Initial Conditions
Incompressible Flows
Compressible Flows
Generalized Galerkin Methods and Taylor-Galerkin Methods
Linearized Burgers’ Equations
Two-Step Explicit Scheme
Relationship between FEM and FDM
Conversion of Implicit Scheme into Explicit Scheme
Taylor-Galerkin Methods for Nonlinear Burgers’ Equations
Numerical Diffusion Test Functions
Derivation of Numerical Diffusion Test Functions
Stability and Accuracy of Numerical Diffusion Test Functions
Discontinuity-Capturing Scheme
Generalized Petrov-Galerkin (GPG) Methods
Generalized Petrov-Galerkin Methods for Unsteady Problems
Space-Time Galerkin/Least Squares Methods Solutions of Nonlinear and Time-Dependent Equations and Element-by-Element Approach
Newton-Raphson Methods
Element-by-Element Solution Scheme for Nonlinear Time Dependent FEM Equations
Generalized Minimal Residual Algorithm
Combined GPE-EBE-GMRES Process
Preconditioning for EBE-GMRES
Example Problems
Nonlinear Wave Equation (Convection Equation)
Pure Convection in Two Dimensions
Solution of 2-D Burgers’ Equation
Summary
References
Incompressible Viscous Flows via Finite Element Methods
Primitive Variable Methods
Mixed Methods
Penalty Methods
Pressure Correction Methods
Generalized Petrov-Galerkin Methods
Operator Splitting Methods
Semi-Implicit Pressure Correction
Vortex Methods
Three-Dimensional Analysis
Two-Dimensional Analysis
Physical Instability in Two-Dimensional Incompressible Flows
Example Problems
Summary
References
Compressible Flows via Finite Element Methods
Governing Equations
Taylor-Galerkin Methods and Generalized Galerkin Methods
Taylor-Galerkin Methods
Taylor-Galerkin Methods with Operator Splitting
Generalized Galerkin Methods
Generalized Petrov-Galerkin Methods
Navier-Stokes System of Equations in Various Variable Forms
The GPG with Conservation Variables
The GPG with Entropy Variables
The GPG with Primitive Variables
Characteristic Galerkin Methods
Discontinuous Galerkin Methods or Combined FEM/FDM/FVM Methods
Flowfield-Dependent Variation Methods
Basic Formulation
Interpretation of FDV Parameters Associated with Jacobians Numerical Diffusion
Transitions and Interactions between Compressible and Incompressible Flows and between Laminar and Turbulent Flows
Finite Element Formulation of FDV Equations
Boundary Conditions
Example Problems
Summary
References
Miscellaneous Weighted Residual Methods
Spectral Element Methods
Spectral Functions
Spectral Element Formulations by Legendre Polynomials
Two-Dimensional Problems
Three-Dimensional Problems
Least Squares Methods
LSM Formulation for the Navier-Stokes System of Equations
FDV-LSM Formulation
Optimal Control Method
Finite Point Method (FPM)
Example Problems
Sharp Fin Induced Shock Wave Boundary Layer Interactions
Asymmetric Double Fin Induced Shock Wave Boundary Layer Interaction
Summary
References
Finite Volume Methods via Finite Element Methods
General
Formulations of Finite Volume Equations
Burgers’ Equations
ncompressible and Compressible Flows
Three-Dimensional Problems
Example Problems
Summary
References
Relationships between Finite Differences and Finite Elements and Other Methods
Simple Comparisons between FDM and FEM
Relationships between FDM and FDV
Relationships between FEM and FDV
Other Methods
Boundary Element Methods
Coupled Eulerian-Lagrangian Methods
cle-in-Cell (PIC) Method
Monte Carlo Methods (MCM)
Summary
References
Automatic Grid Generation, Adaptive Methods, and Computing Techniques
Structured Grid Generation
Algebraic Methods
Unidirectional Interpolation
Multidirectional Interpolation
Domain Vertex Method
Transfinite Interpolation Methods (TFI)
PDE Mapping Methods
Elliptic Grid Generator
Derivation of Governing Equations
Control Functions
Hyperbolic Grid Generator
Cell Area (Jacobian) Method
Arc-Length Method
Parabolic Grid Generator
Surface Grid Generation
Elliptic PDE Methods
Differential Geometry
Surface Grid Generation
Algebraic Methods
Points and Curves
Elementary and Global Surfaces
Surface Mesh Generation
Multiblock Structured Grid Generation
Summary
References
Unstructured Grid Generation
Delaunay-Voronoi Methods
Watson Algorithm
Bowyer Algorithm
Automatic Point Generation Scheme
Advancing Front Methods
Combined DVM and AFM
Three-Dimensional Applications
DVM in 3-D
AFM in 3-D
Curved Surface Grid Generation
Example Problems
Other Approaches
AFM Modified for Quadrilaterals
Iterative Paving Method
Quadtree and Octree Method
Summary
References
Adaptive Methods
Structured Adaptive Methods Control Function Methods
Basic Theory
Weight Functions in One Dimension
Weight Function in Multidimensions
ariational Methods
ariational Formulation
Smoothness Orthogonality and Concentration
Multiblock Adaptive Structured Grid Generation
Unstructured Adaptive Methods
Mesh Refinement Methods ( h-Methods)
Error Indicators
Two-Dimensional Quadrilateral Element
Three-Dimensional Hexahedral Element
Mesh Movement Methods ( r-Methods)
Combined Mesh Refinement and Mesh Movement Methods (hr -Methods)
Mesh Enrichment Methods ( p-Method)
Combined Mesh Refinement and Mesh Enrichment Methods (hp-Methods)
Unstructured Finite Difference Mesh Refinements
Summary
References
Computing Techniques
Domain Decomposition Methods
Multiplicative Schwarz Procedure
Additive Schwarz Procedure
Multigrid Methods
General
Multigrid Solution Procedure on Structured Grids
Multigrid Solution Procedure on Unstructured Grids
Parallel Processing
General
Development of Parallel Algorithms
Parallel Processing with Domain Decomposition and Multigrid Methods
Load Balancing
Example Problems
Solution of Poisson Equation with Domain Decomposition Parallel Processing
Solution of Navier-Stokes System of Equations with Multithreading
Summary
References
Applications
[/i]Applications to Turbulence [/i]
General
Governing Equations
Turbulence Models
Zero-Equation Models
One-Equation Models
Two-Equation Models
Second Order Closure Models (Reynolds Stress Models)
Algebraic Reynolds Stress Models
Compressibility Effects
Large Eddy Simulation
Filtering, Subgrid Scale Stresses, and Energy Spectra
The LES Governing Equations for Compressible Flows
Subgrid Scale Modeling
Direct Numerical Simulation
General
arious Approaches to DNS
Solution Methods and Initial and Boundary Conditions
Applications
Turbulence Models for Reynolds Averaged Navier-Stokes (RANS)
Large Eddy Simulation (LES)
Direct Numerical Simulation (DNS) for Compressible Flows
Summary
References
Applications to Chemically Reactive Flows and Combustion
General
Governing Equations in Reactive Flows
Conservation of Mass for Mixture and Chemical Species
Conservation of Momentum
Conservation of Energy
Conservation Form of Navier-Stokes System of Equations in Reactive Flows
Two-Phase Reactive Flows (Spray Combustion)
Boundary and Initial Conditions
Chemical Equilibrium Computations
Solution Methods of Stiff Chemical Equilibrium Equations
Applications to Chemical Kinetics Calculations
Chemistry-Turbulence Interaction Models
Favre-Averaged Diffusion Flames
Probability Density Functions
Modeling for Energy and Species Equations in Reactive Flows
SGS Combustion Models for LES
Hypersonic Reactive Flows
General
brational and Electronic Energy in Nonequilibrium
Example Problems
Supersonic Inviscid Reactive Flows (Premixed Hydrogen-Air) Turbulent Reactive Flow Analysis with Various RANS Models
PDF Models for Turbulent Diffusion Combustion Analysis
Spectral Element Method for Spatially Developing Mixing Layer
Spray Combustion Analysis with Eulerian-Lagrangian Formulation
LES and DNS Analyses for Turbulent Reactive Flows
Hypersonic Nonequilibrium Reactive Flows with Vibrational and Electronic Energies
Summary
References
Applications to Acoustics
Introduction
Pressure Mode Acoustics
Basic Equations
Kirchhoff’s Method with Stationary Surfaces
Kirchhoff’s Method with Subsonic Surfaces
Kirchhoff’s Method with Supersonic Surfaces
Vorticity Mode Acoustics
Lighthill’s Acoustic Analogy
Ffowcs Williams-Hawkings Equation
Entropy Mode Acoustics
Entropy Energy Governing Equations
Entropy Controlled Instability (ECI) Analysis
Unstable Entropy Waves
Example Problems
Pressure Mode Acoustics
Vorticity Mode Acoustics
Entropy Mode Acoustics
Summary
References
Applications to Combined Mode Radiative Heat Transfer
General
Radiative Heat Transfer
Diffuse Interchange in an Enclosure
View Factors
Radiative Heat Flux and Radiative Transfer Equation
Solution Methods for Integrodifferential Radiative Heat Transfer Equation
Radiative Heat Transfer in Combined Modes
Combined Conduction and Radiation
Combined Conduction, Convection, and Radiation
Three-Dimensional Radiative Heat Flux Integral Formulation
Example Problems
Nonparticipating Media
Solution of Radiative Heat Transfer Equation in Nonparticipating Media
Nonpacipating Media with Conduction and Radiation Participating Media with Conduction, Convection, and Radiation
Three-Dimensional Radiative Heat Flux Integration Formulation
Summary
References
Applications to Multiphase Flows
General
Volume of Fluid Formulation with Continuum Surface Force
Navier-Stokes System of Equations
Surface Tension
Surface and Volume Forces
mplementation of Volume Force
Computational Strategies
Fluid-Particle Mixture Flows
Laminar Flows in Fluid-Particle Mixture with Rigid Body Motions of Solids
Turbulent Flows in Fluid-Particle Mixture
Reactive Turbulent Flows in Fluid-Particle Mixture
Example Problems
Laminar Flows in Fluid-Particle Mixture
Turbulent Flows in Fluid-Particle Mixture
Reactive Turbulent Flows in Fluid-Particle Mixture
Summary
References
Applications to Electromagnetic Flows
Magnetohydrodynamics
Rarefied Gas Dynamics
Basic Equations
Finite Element Solution of Boltzmann Equation
Semiconductor Plasma Processing
Introduction
Charged Particle Kinetics in Plasma Discharge
Discharge Modeling with Moment Equations
Reactor Model for Chemical Vapor Deposition (CVD) Gas Flow
Applications
Applications to Magnetohydrodynamic Flows in Corona Mass Ejection
Applications to Plasma Processing in Semiconductors
Summary
References
Applications to Relativistic Astrophysical Flows
General
Governing Equations in Relativistic Fluid Dynamics
Relativistic Hydrodynamics Equations in Ideal Flows
Relativistic Hydrodynamics Equations in Nonideal Flows
Pseudo-Newtonian Approximations with Gravitational Effects
Example Problems
Relativistic Shock Tube
Black Hole Accretion
Three-Dimensional Relativistic Hydrodynamics
Flowfield Dependent Variation (FDV) Method for Relativistic Astrophysical Flows
Summary
References
Appendixes
A. Three-Dimensional Flux Jacobians
B. Gaussian Quadrature
C. Two Phase Flow – Source Term Jacobians for Surface Tension
D. Relativistic Astrophysical Flow Metrics, Christoffel Symbols, and FDV Flux and Source Term Jacobians
E. Homework Problems
Index
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