Computational Methods for Fluid Dynamics

ISBN-10: 3540420746
ISBN-13: 9783540420743
Edition: 3rd 2002 (Revised)
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Description: In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational  More...

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Book details

List price: $89.95
Edition: 3rd
Copyright year: 2002
Publisher: Springer
Publication date: 11/6/2001
Binding: Paperback
Pages: 426
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.496

In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

Preface
Basic Concepts of Fluid Flow
Introduction
Conservation Principles
Mass Conservation
Momentum Conservation
Conservation of Scalar Quantities
Dimensionless Form of Equations
Simplified Mathematical Models
Incompressible Flow
Inviscid (Euler) Flow
Potential Flow
Creeping (Stokes) Flow
Boussinesq Approximation
Boundary Layer Approximation
Modeling of Complex Flow Phenomena
Mathematical Classification of Flows
Hyperbolic Flows
Parabolic Flows
Elliptic Flows
Mixed Flow Types
Plan of This Book
Introduction to Numerical Methods
Approaches to Fluid Dynamical Problems
What is CFD?
Possibilities and Limitations of Numerical Methods
Components of a Numerical Solution Method
Mathematical Model
Discretization Method
Coordinate and Basis Vector Systems
Numerical Grid
Finite Approximations
Solution Method
Convergence Criteria
Properties of Numerical Solution Methods
Consistency
Stability
Convergence
Conservation
Boundedness
Realizability
Accuracy
Discretization Approaches
Finite Difference Method
Finite Volume Method
Finite Element Method
Finite Difference Methods
Introduction
Basic Concept
Approximation of the First Derivative
Taylor Series Expansion
Polynomial Fitting
Compact Schemes
Non-Uniform Grids
Approximation of the Second Derivative
Approximation of Mixed Derivatives
Approximation of Other Terms
Implementation of Boundary Conditions
The Algebraic Equation System
Discretization Errors
An Introduction to Spectral Methods
Basic Concept
Another View of Discretization Error
Example
Finite Volume Methods
Introduction
Approximation of Surface Integrals
Approximation of Volume Integrals
Interpolation and Differentiation Practices
Upwind Interpolation (UDS)
Linear Interpolation (CDS)
Quadratic Upwind Interpolation (QUICK)
Higher-Order Schemes
Other Schemes
Implementation of Boundary Conditions
The Algebraic Equation System
Examples
Solution of Linear Equation Systems
Introduction
Direct Methods
Gauss Elimination
LU Decomposition
Tridiagonal Systems
Cyclic Reduction
Iterative Methods
Basic Concept
Convergence
Some Basic Methods
Incomplete LU Decomposition: Stone's Method
ADI and Other Splitting Methods
Conjugate Gradient Methods
Biconjugate Gradients and CGSTAB
Multigrid Methods
Other Iterative Solvers
Coupled Equations and Their Solution
Simultaneous Solution
Sequential Solution
Under-Relaxation
Non-Linear Equations and their Solution
Newton-like Techniques
Other Techniques
Deferred-Correction Approaches
Convergence Criteria and Iteration Errors
Examples
Methods for Unsteady Problems
Introduction
Methods for Initial Value Problems in ODEs
Two-Level Methods
Predictor-Corrector and Multipoint Methods
Runge-Kutta Methods
Other Methods
Application to the Generic Transport Equation
Explicit Methods
Implicit Methods
Other Methods
Examples
Solution of the Navier-Stokes Equations
Special Features of the Navier-Stokes Equations
Discretization of Convective and Viscous Terms
Discretization of Pressure Terms and Body Forces
Conservation Properties
Choice of Variable Arrangement on the Grid
Colocated Arrangement
Staggered Arrangements
Calculation of the Pressure
The Pressure Equation and its Solution
A Simple Explicit Time Advance Scheme
A Simple Implicit Time Advance Method
Implicit Pressure-Correction Methods
Other Methods
Fractional Step Methods
Streamfunction-Vorticity Methods
Artificial Compressibility Methods
Solution Methods for the Navier-Stokes Equations
Implicit Scheme Using Pressure-Correction and a Staggered Grid
Treatment of Pressure for Colocated Variables
SIMPLE Algorithm for a Colocated Variable Arrangement
Note on Pressure and Incompressibility
Boundary Conditions for the Navier-Stokes Equations
Examples
Complex Geometries
The Choice of Grid
Stepwise Approximation Using Regular Grids
Overlapping Grids
Boundary-Fitted Non-Orthogonal Grids
Grid Generation
The Choice of Velocity Components
Grid-Oriented Velocity Components
Cartesian Velocity Components
The Choice of Variable Arrangement
Staggered Arrangements
Colocated Arrangement
Finite Difference Methods
Methods Based on Coordinate Transformation
Method Based on Shape Functions
Finite Volume Methods
Approximation of Convective Fluxes
Approximation of Diffusive Fluxes
Approximation of Source Terms
Three-Dimensional Grids
Block-Structured Grids
Unstructured Grids
Control-Volume-Based Finite Element Methods
Pressure-Correction Equation
Axi-Symmetric Problems
Implementation of Boundary Conditions
Inlet
Outlet
Impermeable Walls
Symmetry Planes
Specified Pressure
Examples
Turbulent Flows
Introduction
Direct Numerical Simulation (DNS)
Example: Spatial Decay of Grid Turbulence
Large Eddy Simulation (LES)
Smagorinsky and Related Models
Dynamic Models
Deconvolution Models
Example: Flow Over a Wall-Mounted Cube
Example: Stratified Homogeneous Shear Flow
RANS Models
Reynolds-Averaged Navier-Stokes (RANS) Equations
Simple Turbulence Models and their Application
The v2f Model
Example: Flow Around an Engine Valve
Reynolds Stress Models
Very Large Eddy Simulation
Compressible Flow
Introduction
Pressure-Correction Methods for Arbitrary Mach Number
Pressure-Velocity-Density Coupling
Boundary Conditions
Examples
Methods Designed for Compressible Flow
An Overview of Some Specific Methods
Efficiency and Accuracy Improvement
Error Analysis and Estimation
Description of Errors
Estimation of Errors
Recommended Practice for CFD Uncertainty Analysis
Grid quality and optimization
Multigrid Methods for Flow Calculation
Adaptive Grid Methods and Local Grid Refinement
Parallel Computing in CFD
Iterative Schemes for Linear Equations
Domain Decomposition in Space
Domain Decomposition in Time
Efficiency of Parallel Computing
Special Topics
Introduction
Heat and Mass Transfer
Flows With Variable Fluid Properties
Moving Grids
Free-Surface Flows
Interface-Tracking Methods
Hybrid Methods
Meteorological and Oceanographic Applications
Multiphase flows
Combustion
Appendices
List of Computer Codes and How to Access Them
List of Frequently Used Abbreviations
References
Index

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