流体动力学中的计算方法 第3版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

流体动力学中的计算方法 第3版PDF格式电子书版下载

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1．Basic Concepts of Fluid Flow1

1.1 Introduction1

1.2 Conservation Principles3

1.3 Mass Conservation4

1.4 Momentum Conservation5

1.5 Conservation of Scalar Quantities9

1.6 Dimensionless Form of Equations11

1.7 Simplified Mathematical Models12

1.7.1 Incompressible Flow12

1.7.2 Inviscid(Euler)Flow13

1.7.3 Potential Flow13

1.7.4 Creeping(Stokes)Flow14

1.7.5 Boussinesq Approximation14

1.7.6 Boundary Layer Approximation15

1.7.7 Modeling of Complex Flow Phenomena16

1.8 Mathematical Classification of Flows16

1.8.1 Hyperbolic Flows17

1.8.2 Parabolic Flows17

1.8.3 Elliptic Flows17

1.8.4 Mixed Flow Types18

1.9 Plan of This Book18

2．Introduction to Numerical Methods21

2.1 Approaches to Fluid Dynamical Problems21

2.2 What is CFD?23

2.3 Possibilities and Limitations of Numerical Methods23

2.4 Components of a Numerical Solution Method25

2.4.1 Mathematical Model25

2.4.2 Discretization Method25

2.4.3 Coordinate and Basis Vector Systems26

2.4.4 Numerical Grid26

2.4.5 Finite Approximations30

2.4.6 Solution Method30

2.4.7 Convergence Criteria31

2.5 Properties of Numerical Solution Methods31

2.5.1 Consistency31

2.5.2 Stability32

2.5.3 Convergence32

2.5.4 Conservation33

2.5.5 Boundedness33

2.5.6 Realizability33

2.5.7 Accuracy34

2.6 Discretization Approaches35

2.6.1 Finite Difference Method35

2.6.2 Finite Volume Method36

2.6.3 Finite Element Method36

3．Finite Difference Methods39

3.1 Introduction39

3.2 Basic Concept39

3.3 Approximation of the First Derivative42

3.3.1 Taylor Series Expansion42

3.3.2 Polynomial Fitting44

3.3.3 Compact Schemes45

3.3.4 Non-Uniform Grids47

3.4 Approximation of the Second Derivative49

3.5 Approximation of Mixed Derivatives52

3.6 Approximation of Other Terms53

3.7 Implementation of Boundary Conditions53

3.8 The Algebraic Equation System55

3.9 Discretization Errors58

3.10 An Introduction to Spectral Methods60

3.10.1 Basic Concept60

3.10.2 Another View of Discretization Error62

3.11 Example63

4．Finite Volume Methods71

4.1 Introduction71

4.2 Approximation of Surface Integrals72

4.3 Approximation of Volume Integrals75

4.4 Interpolation and Differentiation Practices76

4.4.1 Upwind Interpolation(UDS)76

4.4.2 Linear Interpolation(CDS)77

4.4.3 Quadratic Upwind Interpolation(QUICK)78

4.4.4 Higher-Order Schemes79

4.4.5 Other Schemes81

4.5 Implementation of Boundary Conditions81

4.6 The Algebraic Equation System82

4.7 Examples82

5．Solution of Linear Equation Systems91

5.1 Introduction91

5.2 Direct Methods92

5.2.1 Gauss Elimination92

5.2.2 LU Decomposition94

5.2.3 Tridiagonal Systems95

5.2.4 Cyclic Reduction96

5.3 Iterative Methods97

5.3.1 Basic Concept97

5.3.2 Convergence98

5.3.3 Some Basic Methods100

5.3.4 Incomplete LU Decomposition:Stone's Method101

5.3.5 ADI and Other Splitting Methods105

5.3.6 Conjugate Gradient Methods107

5.3.7 Biconjugate Gradients and CGSTAB110

5.3.8 Multigrid Methods112

5.3.9 Other Iterative Solvers116

5.4 Coupled Equations and Their Solution116

5.4.1 Simultaneous Solution117

5.4.2 Sequential Solution117

5.4.3 Under-Relaxation118

5.5 Non-Linear Equations and their Solution119

5.5.1 Newton-like Techniques119

5.5.2 Other Techniques121

5.6 Deferred-Correction Approaches122

5.7 Convergence Criteria and Iteration Errors124

5.8 Examples129

6．Methods for Unsteady Problems135

6.1 Introduction135

6.2 Methods for Initial Value Problems in ODEs135

6.2.1 Two-Level Methods135

6.2.2 Predictor-Corrector and Multipoint Methods138

6.2.3 Runge-Kutta Methods140

6.2.4 Other Methods142

6.3 Application to the Generic Transport Equation142

6.3.1 Explicit Methods143

6.3.2 Implicit Methods148

6.3.3 Other Methods151

6.4 Examples152

7．Solution of the Navier-Stokes Equations157

7.1 Special Features of the Navier-Stokes Equations157

7.1.1 Discretization of Convective and Viscous Terms157

7.1.2 Discretization of Pressure Terms and Body Forces158

7.1.3 Conservation Properties160

7.2 Choice of Variable Arrangement on the Grid164

7.2.1 Colocated Arrangement165

7.2.2 Staggered Arrangements166

7.3 Calculation of the Pressure167

7.3.1 The Pressure Equation and its Solution167

7.3.2 A Simple Explicit Time Advance Scheme168

7.3.3 A Simple Implicit Time Advance Method170

7.3.4 Implicit Pressure-Correction Methods172

7.4 Other Methods178

7.4.1 Fractional Step Methods178

7.4.2 Streamfunction-Vorticity Methods181

7.4.3 Artificial Compressibility Methods183

7.5 Solution Methods for the Navier-Stokes Equations188

7.5.1 Implicit Scheme Using Pressure-Correction and a Stag-gered Grid188

7.5.2 Treatment of Pressure for Colocated Variables196

7.5.3 SIMPLE Algorithm for a Colocated Variable Arrange-ment200

7.6 Note on Pressure and Incompressibility202

7.7 Boundary Conditions for the Navier-Stokes Equations204

7.8 Examples206

8．Complex Geometries217

8.1 The Choice of Grid217

8.1.1 Stepwise Approximation Using Regular Grids217

8.1.2 Overlapping Grids218

8.1.3 Boundary-Fitted Non-Orthogonal Grids219

8.2 Grid Generation219

8.3 The Choice of Velocity Components223

8.3.1 Grid-Oriented Velocity Components224

8.3.2 Cartesian Velocity Components224

8.4 The Choice of Variable Arrangement225

8.4.1 Staggered Arrangements225

8.4.2 Colocated Arrangement226

8.5 Finite Difference Methods226

8.5.1 Methods Based on Coordinate Transformation226

8.5.2 Method Based on Shape Functions229

8.6 Finite Volume Methods230

8.6.1 Approximation of Convective Fluxes231

8.6.2 Approximation of Diffusive Fluxes232

8.6.3 Approximation of Source Terms238

8.6.4 Three-Dimensional Grids239

8.6.5 Block-Structured Grids241

8.6.6 Unstructured Grids244

8.7 Control-Volume-Based Finite Element Methods245

8.8 Pressure-Correction Equation247

8.9 Axi-Symmetric Problems252

8.10 Implementation of Boundary Conditions254

8.10.1 Inlet255

8.10.2 Outlet255

8.10.3 Impermeable Walls256

8.10.4 Symmetry Planes258

8.10.5 Specified Pressure258

8.11 Examples259

9．Turbulent Flows265

9.1 Introduction265

9.2 Direct Numerical Simulation(DNS)267

9.2.1 Example:Spatial Decay of Grid Turbulence275

9.3 Large Eddy Simulation(LES)277

9.3.1 Smagorinsky and Related Models279

9.3.2 Dynamic Models281

9.3.3 Deconvolution Models283

9.3.4 Example:Flow Over a Wall-Mounted Cube284

9.3.5 Example:Stratified Homogeneous Shear Flow287

9.4 RANS Models292

9.4.1 Reynolds-Averaged Navier-Stokes(RANS)Equations292

9.4.2 Simple Turbulence Models and their Application294

9.4.3 The v2f Model301

9.4.4 Example:Flow Around an Engine Valve302

9.5 Reynolds Stress Models304

9.6 Very Large Eddy Simulation306

10．Compressible Flow309

10.1 Introduction309

10.2 Pressure-Correction Methods for Arbitrary Mach Number310

10.2.1 Pressure-Velocity-Density Coupling311

10.2.2 Boundary Conditions315

10.2.3 Examples319

10.3 Methods Designed for Compressible Flow324

10.3.1 An Overview of Some Specific Methods326

11．Efficiency and Accuracy Improvement329

11.1 Error Analysis and Estimation329

11.1.1 Description of Errors329

11.1.2 Estimation of Errors332

11.1.3 Recommended Practice for CFD Uncertainty Analysis337

11.2 Grid quality and optimization341

11.3 Multigrid Methods for Flow Calculation344

11.4 Adaptive Grid Methods and Local Grid Refinement351

11.5 Parallel Computing in CFD356

11.5.1 Iterative Schemes for Linear Equations357

11.5.2 Domain Decomposition in Space360

11.5.3 Domain Decomposition in Time363

11.5.4 Efficiency of Parallel Computing364

12．Special Topics369

12.1 Introduction369

12.2 Heat and Mass Transfer370

12.3 Flows With Variable Fluid Properties373

12.4 Moving Grids373

12.5 Free-Surface Flows381

12.5.1 Interface-Tracking Methods388

12.5.2 Hybrid Methods396

12.6 Meteorological and Oceanographic Applications397

12.7 Multiphase flows399

12.8 Combustion400

A．Appendices405

A.1 List of Computer Codes and How to Access Them405

A.2 List of Frequently Used Abbreviations407

References409

Index421