search for books and compare prices
Tables of Contents for Computational Fluid Mechanics and Heat Transfer
Chapter/Section Title
Page #
Page Count
Preface
xv
4
Preface to the First Edition
xix
Part I Fundamentals
1
246
1 INTRODUCTION
3
12
1.1 General Remarks
3
2
1.2 Comparison of Experimental, Theoretical, and Computational Approaches
5
5
1.3 Historical Perspective
10
5
2 PARTIAL DIFFERENTIAL EQUATIONS
15
30
2.1 Introduction
15
1
2.2 Physical Classification
15
7
2.2.1 Equilibrium Problems
15
4
2.2.2 Marching Problems
19
3
2.3 Mathematical Classification
22
11
2.3.1 Hyperbolic PDEs
26
3
2.3.2 Parabolic PDEs
29
3
2.3.3 Elliptic PDEs
32
1
2.4 The Well-Posed Problem
33
2
2.5 Systems of Equations
35
5
2.6 Other Differential Equations of Interest
40
1
Problems
41
4
3 BASICS OF DISCRETIZATION METHODS
45
56
3.1 Introduction
45
1
3.2 Finite Differences
46
6
3.3 Difference Representation of Partial Differential Equations
52
8
3.3.1 Truncation Error
52
2
3.3.2 Round-Off and Discretization Errors
54
1
3.3.3 Consistency
55
1
3.3.4 Stability
55
2
3.3.5 Convergence for Marching Problems
57
1
3.3.6 A Comment on Equilibrium Problems
57
1
3.3.7 Conservation Form and Conservative Property
58
2
3.4 Further Examples of Methods for Obtaining Finite-Difference Equations
60
16
3.4.1 Use of Taylor Series
61
4
3.4.2 Use of Polynomial Fitting
65
4
3.4.3 Integral Method
69
2
3.4.4 Finite-Volume (Control-Volume) Approach
71
5
3.5 Introduction to the Use of Irregular Meshes
76
7
3.5.1 Irregular Mesh Due to Shape of a Boundary
76
6
3.5.2 Irregular Mesh Not Caused by Shape of a Boundary
82
1
3.5.3 Concluding Remarks
83
1
3.6 Stability Considerations
83
13
3.6.1 Fourier or von Neumann Analysis
84
7
3.6.2 Stability Analysis for Systems of Equations
91
5
Problems
96
5
4 APPLICATION OF NUMERICAL METHODS TO SELECTED MODEL EQUATIONS
101
148
4.1 Wave Equation
102
24
4.1.1 Euler Explicit Methods
102
1
4.1.2 Upstream (First-Order Upwind or Windward) Differencing Method
103
14
4.1.3 Lax Method
112
1
4.1.4 Euler Implicit Method
113
3
4.1.5 Leap Frog Method
116
1
4.1.6 Lax-Wendroff Method
117
1
4.1.7 Two-Step Lax-Wendroff Method
118
1
4.1.8 MacCormack Method
119
1
4.1.9 Second-Order Upwind Method
119
1
4.1.10 Time-Centered Implicit Method (Trapezoidal Differencing Method)
120
2
4.1.11 Rusanov (Burstein-Mirin) Method
122
1
4.1.12 Warming-Kutler-Lomax Method
123
1
4.1.13 Runge-Kutta Methods
124
1
4.1.14 Additional Comments
125
1
4.2 Heat Equation
126
18
4.2.1 Simple Explicit Method
126
3
4.2.2 Richardson's Method
129
1
4.2.3 Simple Implicit (Laasonen) Method
130
1
4.2.4 Crank-Nicolson Method
130
2
4.2.5 Combined Method A
132
1
4.2.6 Combined Method B
132
1
4.2.7 DuFort-Frankel Method
133
1
4.2.8 Keller Box and Modified Box Methods
134
3
4.2.9 Methods for the Two-Dimensional Heat Equation
137
2
4.2.10 ADI Methods
139
2
4.2.11 Splitting or Fractional-Step Methods
141
1
4.2.12 ADE Methods
142
1
4.2.13 Hopscotch Method
143
1
4.2.14 Additional Comments
144
1
4.3 Laplace's Equation
144
32
4.3.1 Finite-Difference Representations for Laplace's Equation
145
1
4.3.2 Simple Example for Laplace's Equation
146
2
4.3.3 Direct Methods for Solving Systems of Linear Algebraic Equations
148
5
4.3.4 Iterative Methods for Solving Systems of Linear Algebraic Equations
153
12
4.3.5 Multigrid Method
165
11
4.4 Burgers' Equation (Inviscid)
176
41
4.4.1 Lax Method
181
3
4.4.2 Lax-Wendroff Method
184
3
4.4.3 MacCormack Method
187
1
4.4.4 Rusanov (Burstein-Mirin) Method
188
1
4.4.5 Warming-Kutler-Lomax Method
189
1
4.4.6 Tuned Third-Order Methods
190
2
4.4.7 Implicit Methods
192
3
4.4.8 Godunov Scheme
195
3
4.4.9 Roe Scheme
198
4
4.4.10 Enquist-Osher Scheme
202
2
4.4.11 Higher-Order Upwind Schemes
204
3
4.4.12 TVD Schemes
207
10
4.5 Burgers' Equation (Viscous)
217
17
4.5.1 FTCS Method
220
5
4.5.2 Leap Frog/DuFort-Frankel Method
225
1
4.5.3 Brailovskaya Method
225
1
4.5.4 Allen-Cheng Method
226
1
4.5.5 Lax-Wendroff Method
227
1
4.5.6 MacCormack Method
227
2
4.5.7 Briley-McDonald Method
229
1
4.5.8 Time-Split MacCormack Method
230
2
4.5.9 ADI Methods
232
1
4.5.10 Predictor-Corrector, Multiple-Iteration Method
232
1
4.5.11 Roe Method
233
1
4.6 Concluding Remarks
234
1
Problems
234
13
Part II Application of Numerical Methods to the Equations of Fluid Mechanics and Heat Transfer
247
468
5 GOVERNING EQUATIONS OF FLUID MECHANICS AND HEAT TRANSFER
249
102
5.1 Fundamental Equations
249
23
5.1.1 Continuity Equation
250
2
5.1.2 Momentum Equation
252
3
5.1.3 Energy Equation
255
2
5.1.4 Equation of State
257
2
5.1.5 Chemically Reacting Flows
259
4
5.1.6 Vector Form of Equations
263
1
5.1.7 Nondimensional Form of Equations
264
2
5.1.8 Orthogonal Curvilinear Coordinates
266
6
5.2 Averaged Equations for Turbulent Flows
272
13
5.2.1 Background
272
1
5.2.2 Reynolds Averaged Navier-Stokes Equations
273
2
5.2.3 Reynolds Form of the Continuity Equation
275
1
5.2.4 Reynolds Form of the Momentum Equations
276
2
5.2.5 Reynolds Form of the Energy Equation
278
2
5.2.6 Comments on the Reynolds Equations
280
3
5.2.7 Filtered Navier-Stokes Equations for Large-Eddy Simulation
283
2
5.3 Boundary-Layer Equations
285
14
5.3.1 Background
285
1
5.3.2 Boundary-Layer Approximation for Steady Incompressible Flow
286
9
5.3.3 Boundary-Layer Equations for Compressible Flow
295
4
5.4 Introduction to Turbulence Modeling
299
22
5.4.1 Background
299
1
5.4.2 Modeling Terminology
299
2
5.4.3 Simple Algebraic or Zero-Equation Models
301
7
5.4.4 One-Half-Equation Models
308
2
5.4.5 One-Equation Models
310
3
5.4.6 One-and-One-Half and Two-Equation Models
313
4
5.4.7 Reynolds Stress Models
317
3
5.4.8 Subgrid-Scale Models for Large-Eddy Simulation
320
1
5.5 Euler Equations
321
12
5.5.1 Continuity Equation
322
1
5.5.2 Inviscid Momentum Equations
323
3
5.5.3 Inviscid Energy Equations
326
1
5.5.4 Additional Equations
327
1
5.5.5 Vector Form of Euler Equations
328
1
5.5.6 Simplified Forms of Euler Equations
329
2
5.5.7 Shock Equations
331
2
5.6 Transformation of Governing Equations
333
9
5.6.1 Simple Transformations
333
5
5.6.2 Generalized Transformation
338
4
5.7 Finite-Volume Formulation
342
6
5.7.1 Two-Dimensional Finite-Volume Method
342
5
5.7.2 Three-Dimensional Finite-Volume Method
347
1
Problems
348
3
6 NUMERICAL METHODS FOR INVISCID FLOW EQUATIONS
351
90
6.1 Introduction
351
1
6.2 Method of Characteristics
352
13
6.2.1 Linear Systems of Equations
353
8
6.2.2 Nonlinear Systems of Equations
361
4
6.3 Classical Shock-Capturing Methods
365
10
6.4 Flux Splitting Schemes
375
11
6.4.1 Steger-Warming Splitting
376
5
6.4.2 Van Leer Flux Splitting
381
2
6.4.3 Other Flux Splitting Schemes
383
2
6.4.4 Application for Arbitrarily Shaped Cells
385
1
6.5 Flux-Difference Splitting Schemes
386
12
6.5.1 Roe Scheme
388
7
6.5.2 Second-Order Schemes
395
3
6.6 Multidimensional Case in a General Coordinate System
398
4
6.7 Boundary Conditions for the Euler Equations
402
11
6.8 Methods for Solving the Potential Equation
413
15
6.9 Transonic Small-Disturbance Equations
428
3
6.10 Methods for Solving Laplace's Equation
431
6
Problems
437
4
7 NUMERICAL METHODS FOR BOUNDARY-LAYER TYPE EQUATIONS
441
96
7.1 Introduction
441
1
7.2 Brief Comparison of Prediction Methods
442
1
7.3 Finite-Difference Methods for Two-Dimensional or Axisymmetric Steady External Flows
443
35
7.3.1 Generalized Form of the Equations
443
2
7.3.2 Example of a Simple Explicit Procedure
445
2
7.3.3 Crank-Nicolson and Fully Implicit Methods
447
12
7.3.4 DuFort-Frankel Method
459
3
7.3.5 Box Method
462
3
7.3.6 Other Methods
465
1
7.3.7 Coordinate Transformations for Boundary Layers
466
4
7.3.8 Special Considerations for Turbulent Flows
470
3
7.3.9 Example Applications
473
3
7.3.10 Closure
476
2
7.4 Inverse Methods, Separated Flows, and Viscous-Inviscid Interaction
478
18
7.4.1 Introduction
478
1
7.4.2 Comments on Computing Separated Flows Using the Boundary-Layer Equations
479
3
7.4.3 Inverse Finite-Difference Methods
482
7
7.4.4 Viscous-Inviscid Interaction
489
7
7.5 Methods for Internal Flows
496
12
7.5.1 Introduction
496
2
7.5.2 Coordinate Transformation for Internal Flows
498
1
7.5.3 Computational Strategies for Internal Flows
498
10
7.5.4 Additional Remarks
508
1
7.6 Application to Free-Shear Flows
508
4
7.7 Three-Dimensional Boundary Layers
512
18
7.7.1 Introduction
512
1
7.7.2 The Equations
513
6
7.7.3 Comments on Solution Methods for Three-Dimensional Flows
519
9
7.7.4 Example Calculations
528
2
7.7.5 Additional Remarks
530
1
7.8 Unsteady Boundary Layers
530
2
Problems
532
5
8 NUMERICAL METHODS FOR THE "PARABOLIZED" NAVIER-STOKES EQUATIONS
537
84
8.1 Introduction
537
4
8.2 Thin-Layer Navier-Stokes Equations
541
4
8.3 "Parabolized" Navier-Stokes Equations
545
40
8.3.1 Derivation of PNS Equations
546
9
8.3.2 Streamwise Pressure Gradient
555
7
8.3.3 Numerical Solution of PNS Equations
562
20
8.3.4 Applications of PNS Equations
582
3
8.4 Parabolized and Partially Parabolized Navier-Stokes Procedures for Subsonic Flows
585
24
8.4.1 Fully Parabolic Procedures
585
7
8.4.2 Parabolic Procedures for 3-D Free-Shear and Other Flows
592
1
8.4.3 Partially Parabolized (Multiple Space-Marching) Model
593
16
8.5 Viscous Shock-Layer Equations
609
5
8.6 "Conical" Navier-Stokes Equations
614
3
Problems
617
4
9 NUMERICAL METHODS FOR THE NAVIER-STOKES EQUATIONS
621
58
9.1 Introduction
621
1
9.2 Compressible Navier-Stokes Equations
622
27
9.2.1 Explicit MacCormack Method
625
7
9.2.2 Other Explicit Methods
632
1
9.2.3 Beam-Warming Scheme
633
7
9.2.4 Other Implicit Methods
640
1
9.2.5 Upwind Methods
641
1
9.2.6 Compressible Navier-Stokes Equations at Low Speeds
642
7
9.3 Incompressible Navier-Stokes Equations
649
28
9.3.1 Vorticity-Stream Function Approach
650
9
9.3.2 Primitive-Variable Approach
659
18
Problems
677
2
10 GRID GENERATION
679
36
10.1 Introduction
679
2
10.2 Algebraic Methods
681
7
10.3 Differential Equation Methods
688
10
10.3.1 Elliptic Schemes
688
6
10.3.2 Hyperbolic Schemes
694
3
10.3.3 Parabolic Schemes
697
1
10.4 Variational Methods
698
2
10.5 Unstructured Grid Schemes
700
8
10.5.1 Connectivity Information
702
1
10.5.2 Delaunay Triangulation
703
2
10.5.3 Bowyer Algorithm
705
3
10.6 Other Approaches
708
2
10.7 Adaptive Grids
710
2
Problems
712
3
APPENDIXES
715
1
A Subroutine for Solving a Tridiagonal System of Equations
715
2
B Subroutines for Solving Block Tridiagonal Systems of Equations
717
8
C The Modified Strongly Implicit Procedure
725
6
D Finite-Volume Discretization for General Control Volumes
731
6
NOMENCLATURE
737
8
REFERENCES
745
38
INDEX
783