Computational Methods for Fluid Dynamics

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ISBN: 9783540420743 | 3540420746
Cover: Paperback
Copyright: 12/1/2001

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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	p. V
Basic Concepts of Fluid Flow	p. 1
Introduction	p. 1
Conservation Principles	p. 3
Mass Conservation	p. 4
Momentum Conservation	p. 5
Conservation of Scalar Quantities	p. 9
Dimensionless Form of Equations	p. 11
Simplified Mathematical Models	p. 12
Incompressible Flow	p. 12
Inviscid (Euler) Flow	p. 13
Potential Flow	p. 13
Creeping (Stokes) Flow	p. 14
Boussinesq Approximation	p. 14
Boundary Layer Approximation	p. 15
Modeling of Complex Flow Phenomena	p. 16
Mathematical Classification of Flows	p. 16
Hyperbolic Flows	p. 17
Parabolic Flows	p. 17
Elliptic Flows	p. 17
Mixed Flow Types	p. 18
Plan of This Book	p. 18
Introduction to Numerical Methods	p. 21
Approaches to Fluid Dynamical Problems	p. 21
What is CFD?	p. 23
Possibilities and Limitations of Numerical Methods	p. 23
Components of a Numerical Solution Method	p. 25
Mathematical Model	p. 25
Discretization Method	p. 25
Coordinate and Basis Vector Systems	p. 26
Numerical Grid	p. 26
Finite Approximations	p. 30
Solution Method	p. 30
Convergence Criteria	p. 31
Properties of Numerical Solution Methods	p. 31
Consistency	p. 31
Stability	p. 32
Convergence	p. 32
Conservation	p. 33
Boundedness	p. 33
Realizability	p. 33
Accuracy	p. 34
Discretization Approaches	p. 35
Finite Difference Method	p. 35
Finite Volume Method	p. 36
Finite Element Method	p. 36
Finite Difference Methods	p. 39
Introduction	p. 39
Basic Concept	p. 39
Approximation of the First Derivative	p. 42
Taylor Series Expansion	p. 42
Polynomial Fitting	p. 44
Compact Schemes	p. 45
Non-Uniform Grids	p. 47
Approximation of the Second Derivative	p. 49
Approximation of Mixed Derivatives	p. 52
Approximation of Other Terms	p. 53
Implementation of Boundary Conditions	p. 53
The Algebraic Equation System	p. 55
Discretization Errors	p. 58
An Introduction to Spectral Methods	p. 60
Basic Concept	p. 60
Another View of Discretization Error	p. 62
Example	p. 63
Finite Volume Methods	p. 71
Introduction	p. 71
Approximation of Surface Integrals	p. 72
Approximation of Volume Integrals	p. 75
Interpolation and Differentiation Practices	p. 76
Upwind Interpolation (UDS)	p. 76
Linear Interpolation (CDS)	p. 77
Quadratic Upwind Interpolation (QUICK)	p. 78
Higher-Order Schemes	p. 79
Other Schemes	p. 81
Implementation of Boundary Conditions	p. 81
The Algebraic Equation System	p. 82
Examples	p. 82
Solution of Linear Equation Systems	p. 91
Introduction	p. 91
Direct Methods	p. 92
Gauss Elimination	p. 92
LU Decomposition	p. 94
Tridiagonal Systems	p. 95
Cyclic Reduction	p. 96
Iterative Methods	p. 97
Basic Concept	p. 97
Convergence	p. 98
Some Basic Methods	p. 100
Incomplete LU Decomposition: Stone's Method	p. 101
ADI and Other Splitting Methods	p. 105
Conjugate Gradient Methods	p. 107
Biconjugate Gradients and CGSTAB	p. 110
Multigrid Methods	p. 112
Other Iterative Solvers	p. 116
Coupled Equations and Their Solution	p. 116
Simultaneous Solution	p. 117
Sequential Solution	p. 117
Under-Relaxation	p. 118
Non-Linear Equations and their Solution	p. 119
Newton-like Techniques	p. 119
Other Techniques	p. 121
Deferred-Correction Approaches	p. 122
Convergence Criteria and Iteration Errors	p. 124
Examples	p. 129
Methods for Unsteady Problems	p. 135
Introduction	p. 135
Methods for Initial Value Problems in ODEs	p. 135
Two-Level Methods	p. 135
Predictor-Corrector and Multipoint Methods	p. 138
Runge-Kutta Methods	p. 140
Other Methods	p. 142
Application to the Generic Transport Equation	p. 142
Explicit Methods	p. 143
Implicit Methods	p. 148
Other Methods	p. 151
Examples	p. 152
Solution of the Navier-Stokes Equations	p. 157
Special Features of the Navier-Stokes Equations	p. 157
Discretization of Convective and Viscous Terms	p. 157
Discretization of Pressure Terms and Body Forces	p. 158
Conservation Properties	p. 160
Choice of Variable Arrangement on the Grid	p. 164
Colocated Arrangement	p. 165
Staggered Arrangements	p. 166
Calculation of the Pressure	p. 167
The Pressure Equation and its Solution	p. 167
A Simple Explicit Time Advance Scheme	p. 168
A Simple Implicit Time Advance Method	p. 170
Implicit Pressure-Correction Methods	p. 172
Other Methods	p. 178
Fractional Step Methods	p. 178
Streamfunction-Vorticity Methods	p. 181
Artificial Compressibility Methods	p. 183
Solution Methods for the Navier-Stokes Equations	p. 188
Implicit Scheme Using Pressure-Correction and a Staggered Grid	p. 188
Treatment of Pressure for Colocated Variables	p. 196
SIMPLE Algorithm for a Colocated Variable Arrangement	p. 200
Note on Pressure and Incompressibility	p. 202
Boundary Conditions for the Navier-Stokes Equations	p. 204
Examples	p. 206
Complex Geometries	p. 217
The Choice of Grid	p. 217
Stepwise Approximation Using Regular Grids	p. 217
Overlapping Grids	p. 218
Boundary-Fitted Non-Orthogonal Grids	p. 219
Grid Generation	p. 219
The Choice of Velocity Components	p. 223
Grid-Oriented Velocity Components	p. 224
Cartesian Velocity Components	p. 224
The Choice of Variable Arrangement	p. 225
Staggered Arrangements	p. 225
Colocated Arrangement	p. 226
Finite Difference Methods	p. 226
Methods Based on Coordinate Transformation	p. 226
Method Based on Shape Functions	p. 229
Finite Volume Methods	p. 230
Approximation of Convective Fluxes	p. 231
Approximation of Diffusive Fluxes	p. 232
Approximation of Source Terms	p. 238
Three-Dimensional Grids	p. 239
Block-Structured Grids	p. 241
Unstructured Grids	p. 244
Control-Volume-Based Finite Element Methods	p. 245
Pressure-Correction Equation	p. 247
Axi-Symmetric Problems	p. 252
Implementation of Boundary Conditions	p. 254
Inlet	p. 255
Outlet	p. 255
Impermeable Walls	p. 256
Symmetry Planes	p. 258
Specified Pressure	p. 258
Examples	p. 259
Turbulent Flows	p. 265
Introduction	p. 265
Direct Numerical Simulation (DNS)	p. 267
Example: Spatial Decay of Grid Turbulence	p. 275
Large Eddy Simulation (LES)	p. 277
Smagorinsky and Related Models	p. 279
Dynamic Models	p. 281
Deconvolution Models	p. 283
Example: Flow Over a Wall-Mounted Cube	p. 284
Example: Stratified Homogeneous Shear Flow	p. 287
RANS Models	p. 292
Reynolds-Averaged Navier-Stokes (RANS) Equations	p. 292
Simple Turbulence Models and their Application	p. 294
The v2f Model	p. 301
Example: Flow Around an Engine Valve	p. 302
Reynolds Stress Models	p. 304
Very Large Eddy Simulation	p. 306
Compressible Flow	p. 309
Introduction	p. 309
Pressure-Correction Methods for Arbitrary Mach Number	p. 310
Pressure-Velocity-Density Coupling	p. 311
Boundary Conditions	p. 315
Examples	p. 319
Methods Designed for Compressible Flow	p. 324
An Overview of Some Specific Methods	p. 326
Efficiency and Accuracy Improvement	p. 329
Error Analysis and Estimation	p. 329
Description of Errors	p. 329
Estimation of Errors	p. 332
Recommended Practice for CFD Uncertainty Analysis	p. 337
Grid quality and optimization	p. 341
Multigrid Methods for Flow Calculation	p. 344
Adaptive Grid Methods and Local Grid Refinement	p. 351
Parallel Computing in CFD	p. 356
Iterative Schemes for Linear Equations	p. 357
Domain Decomposition in Space	p. 360
Domain Decomposition in Time	p. 363
Efficiency of Parallel Computing	p. 364
Special Topics	p. 369
Introduction	p. 369
Heat and Mass Transfer	p. 370
Flows With Variable Fluid Properties	p. 373
Moving Grids	p. 373
Free-Surface Flows	p. 381
Interface-Tracking Methods	p. 388
Hybrid Methods	p. 396
Meteorological and Oceanographic Applications	p. 397
Multiphase flows	p. 399
Combustion	p. 400
Appendices	p. 405
List of Computer Codes and How to Access Them	p. 405
List of Frequently Used Abbreviations	p. 407
References	p. 409
Index	p. 421
Table of Contents provided by Syndetics. All Rights Reserved.

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