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Computational Fluid Mechanics and Heat Transfer, Third Edition,9781560320463
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Computational Fluid Mechanics and Heat Transfer, Third Edition


Edition: 2nd
Author(s): Pletcher,Richard
ISBN10:  156032046X
ISBN13:  9781560320463
Format:  Hardcover
Pub. Date:  4/1/1997
Publisher(s): Taylor & Franci

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SummaryTable of Contents
This classic text has been thoroughly updated to include all the latest developments while still preserving the fundamental ideas covered in the first edition. Ninety-five new homework problems have been added to further enhance the student's understanding of the fundamentals and applications and to stress the practical application of the text material.
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

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