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Computational Fluid Dynamics for Incompressible Flows [Kõva köide]

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  • Formaat: Hardback, 416 pages, kõrgus x laius: 234x156 mm, kaal: 712 g, 19 Tables, black and white; 100 Illustrations, black and white
  • Ilmumisaeg: 21-Aug-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367408066
  • ISBN-13: 9780367408060
Teised raamatud teemal:
Computational Fluid Dynamics for Incompressible FlowsSuurem pilt
  • Formaat: Hardback, 416 pages, kõrgus x laius: 234x156 mm, kaal: 712 g, 19 Tables, black and white; 100 Illustrations, black and white
  • Ilmumisaeg: 21-Aug-2020
  • Kirjastus: CRC Press
  • ISBN-10: 0367408066
  • ISBN-13: 9780367408060
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367408060.html
Märksõnad:
"This textbook covers fundamental and advanced concepts of computational fluid dynamics, a powerful and essential tool for fluid flow analysis. It discusses various governing equations used in computational fluid dynamics, their derivations, and the physical and mathematical significance of partial differential equations and the boundary conditions. It covers fundamental concepts of finite difference and finite volume methods for diffusion, convection-diffusion problems both for cartesian and non-orthogonal grids. The solution of algebraic equations arising due to finite difference and finite volume discretization are highlighted using direct and iterative methods. Pedagogical features including solved problems and unsolved exercises are interspersed throughout the text for better understanding. The textbook is primarily written for senior undergraduate and graduate students in the field of mechanical engineering and aerospace engineering, for a course on computational fluid dynamics and heat transfer. The textbook will be accompanied by teaching resources including solution manual for the instructors"--

This textbook covers fundamental and advanced concepts of computational fluid dynamics, a powerful and essential tool for fluid flow analysis. It discusses various governing equations used in the field, their derivations, and the physical and mathematical significance of partial differential equations and the boundary conditions. It covers fundamental concepts of finite difference and finite volume methods for diffusion, convection-diffusion problems both for cartesian and non-orthogonal grids. The solution of algebraic equations arising due to finite difference and finite volume discretization are highlighted using direct and iterative methods. Pedagogical features including solved problems and unsolved exercises are interspersed throughout the text for better understanding. The textbook is primarily written for senior undergraduate and graduate students in the field of mechanical engineering and aerospace engineering, for a course on computational fluid dynamics and heat transfer. The textbook will be accompanied by teaching resources including a solution manual for the instructors.

  • Written clearly and with sufficient foundational background to strengthen fundamental knowledge of the topic.

  • Offers a detailed discussion of both finite difference and finite volume methods.

  • Discusses various higher-order bounded convective schemes, TVD discretisation schemes based on the flux limiter essential for a general purpose CFD computation.

  • Discusses algorithms connected with pressure-linked equations for incompressible flow.

  • Covers turbulence modelling like k-e, k-?, SST k- , Reynolds Stress Transport models.

  • A separate chapter on best practice guidelines is included to help CFD practitioners.

Preface xix
Acknowledgements xxiii
Chapter 1 Overview of CFD
1(8)
1.1 Introduction
1(1)
1.2 Basic Principles of CFD
2(1)
1.3 What Does a CFD Algorithm Do?
2(1)
1.4 Stages of a CFD Analysis
3(2)
1.4.1 Pre-Processor
3(1)
1.4.2 Solver
4(1)
1.4.3 Post-Processor
4(1)
1.5 Governing Equations
5(1)
1.6 Discretization
5(1)
1.6.1 Finite Difference Method
5(1)
1.6.2 Finite Volume Method
5(1)
1.6.3 Finite Element Method
5(1)
1.7 Discretization Properties
6(1)
Questions
7(2)
Chapter 2 Governing Equations and Classification of PDE
9(24)
Governing Equations
9(1)
2.1 Introduction
9(1)
2.1.1 Integral Form
9(1)
2.1.2 Differential Form
9(1)
2.2 Conservative Form of the Flow Equations
9(15)
2.2.1 Mass (Continuity)
9(1)
2.2.1.1 Derivation of Continuity Equation
10(2)
2.2.2 Momentum Equations
12(1)
2.2.2.1 Derivation of X-Momentum Equation
13(3)
2.2.3 Energy Equation
16(2)
2.2.3.1 Derivation of Energy Equation
18(5)
2.2.4 General Scalar
23(1)
2.3 Some Comments
24(1)
2.3.1 Conservative and Non-Conservative Forms of Equations
24(1)
2.3.2 Compressible and Incompressible Flow
24(1)
Physical and Mathematical Classification of Partial Differential Equations
25(1)
2.4 Equilibrium Problems
25(1)
2.5 Marching Problems
25(1)
2.6 Mathematical Classification
26(1)
2.7 Important Equations
27(1)
2.8 Boundary Conditions (BCs)
28(2)
2.8.1 Inlet Boundary
29(1)
2.8.1.1 Inflow
29(1)
2.8.1.2 Stagnation (Reservoir)
29(1)
2.8.2 Outlet Boundary
29(1)
2.8.2.1 Outflow
29(1)
2.8.2.2 Pressure
29(1)
2.8.2.3 Radiation (Convection)
29(1)
2.8.3 Wall Boundaries
29(1)
2.8.3.1 No-Slip Wall
29(1)
2.8.3.2 Slip Wall
29(1)
2.8.4 Other Boundary Conditions
30(1)
2.8.4.1 Symmetry Plane and Axis Boundary
30(1)
2.8.4.2 Periodic
30(1)
2.9 Summary
30(1)
Questions
30(3)
Chapter 3 Finite Difference Method: Fundamentals
33(16)
3.1 Introduction
33(1)
3.2 Taylor Series Expansion
34(4)
3.3 Unequal Grid Spacing
38(1)
3.4 Difference Representation of PDE
39(5)
3.4.1 Errors
39(1)
3.4.1.1 Truncation Error
39(1)
3.4.1.2 Round-off Error
40(1)
3.4.2 Consistency
40(1)
3.4.3 Stability
41(1)
3.4.3.1 Von Neumann's Method
42(1)
3.4.4 Convergence
43(1)
3.4.5 Lax's Equivalence Theorem
43(1)
3.4.6 Courant Number
44(1)
3.5 Examples
44(2)
3.6 Summary
46(1)
Questions
46(3)
Chapter 4 Finite Difference Method: Application
49(62)
4.1 Introduction
49(1)
4.2 One-Dimensional Diffusion Equations
49(12)
4.2.1 Explicit Methods
50(1)
4.2.1.1 The Forward Time, Central Space
50(1)
4.2.1.2 The Richardson's Method
51(2)
4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method)
53(2)
4.2.2 Implicit Methods
55(1)
4.2.2.1 The Classical Implicit Method
55(2)
4.2.2.2 The Crank-Nicolson Method
57(3)
4.2.2.3 The Method of Weighted Averages
60(1)
4.3 One-Dimensional Transport Equations
61(12)
4.3.1 The Wave Equation
62(1)
4.3.1.1 The FTCS Method
62(1)
4.3.1.2 Upwind Differencing
63(3)
4.3.1.3 The Lax Method (Lax-Friedrichs Method)
66(1)
4.3.1.4 The Lax-Wendroff Method
67(1)
4.3.1.5 The Two-Step Lax-Wendroff Method
68(1)
4.3.1.6 The MacCormack Method
68(1)
4.3.1.7 The Beam-Warming Method
69(1)
4.3.1.8 The Implicit Method
70(1)
4.3.2 The Complete Transport Equation
71(1)
4.3.2.1 Central Difference
71(1)
4.3.2.2 The Richardson Method
72(1)
4.3.2.3 The DuFort-Frankel Method
72(1)
4.3.2.4 The Upwind Method
73(1)
4.4 Two-Dimensional Diffusion Equation
73(6)
4.4.1 The Explicit Method
74(1)
4.4.2 Implicit Methods
75(1)
4.4.2.1 The Fully Implicit Method
75(1)
4.4.2.2 The Crank-Nicolson Method
75(1)
4.4.2.3 The Alternate Direction Implicit (ADI) Method
75(2)
4.4.2.4 Comments on Diffusion Equations
77(1)
4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables
77(1)
4.4.2.6 The Grid (Mesh) Independence Study
78(1)
4.5 Burgers' Equation
79(16)
4.5.1 The Inviscid Burgers' Equation
81(1)
4.5.1.1 Upwind Differencing
81(1)
4.5.1.2 The Lax (Lax-Friedrichs) Method
81(1)
4.5.1.3 The Lax-Wendroff Method
82(1)
4.5.1.4 The MacCormack Method
83(1)
4.5.1.5 Implicit Methods
84(1)
4.5.1.6 The Godunov Method
84(5)
4.5.1.7 The Roe Method
89(3)
4.5.2 The Viscid Burgers' Equation
92(1)
4.5.2.1 The FTCS Method
93(1)
4.5.2.2 The DuFort-Frankel Method
93(1)
4.5.2.3 The Lax-Wendroff Method
94(1)
4.5.2.4 The MacCormack Method
94(1)
4.6 The Laplace Equation
95(1)
4.7 Examples
95(12)
4.8 Summary
107(1)
Questions
107(4)
Chapter 5 Finite Volume Method
111(70)
5.1 Introduction
111(1)
5.2 The Diffusion Equation
112(9)
5.2.1 The Steady-State One-Dimensional Diffusion Equation
113(2)
5.2.2 Discretization of the Source Term
115(1)
5.2.3 Discretized Equation at Boundaries
116(1)
5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions)
116(1)
5.2.3.2 Insulated Boundary
116(1)
5.2.3.3 Mixed Boundary Conditions
117(1)
5.2.4 Assembling the Algebraic Equations
117(1)
5.2.5 Extension to Two Dimensions
118(1)
5.2.6 Extension to Three Dimensions
119(1)
5.2.7 Desirable Properties of a Discretization Scheme
119(1)
5.2.8 Further Comments on Interface Diffusion Coefficients
120(1)
5.3 The Convection-Diffusion Equation
121(36)
5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation
122(1)
5.3.1.1 The Central Differencing Scheme
122(2)
5.3.1.2 The Upwind Differencing Scheme
124(3)
5.3.1.3 Exact Solution
127(1)
5.3.1.4 The Exponential Scheme
128(1)
5.3.1.5 The Hybrid Differencing Scheme
129(1)
5.3.1.6 The Second Order Upwind (SOU) Scheme
130(2)
5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme
132(1)
5.3.1.8 The FROMM Scheme
133(2)
5.3.1.9 Advantages and Disadvantages of Various Convective Schemes
135(1)
5.3.2 Deferred Correction Approach
135(1)
5.3.2.1 CDS
136(1)
5.3.2.2 SOU
137(1)
5.3.2.3 QUICK
138(1)
5.3.2.4 FROMM
139(1)
5.3.3 Extension to Two Dimension
140(1)
5.3.3.1 UDS
141(1)
5.3.3.2 CDS
142(1)
5.3.3.3 SOU
143(1)
5.3.3.4 QUICK
144(1)
5.3.3.5 FROMM
145(1)
5.3.4 Extension to Three Dimension
146(1)
5.3.4.1 UDS
147(1)
5.3.4.2 CDS
147(1)
5.3.4.3 SOU
147(1)
5.3.4.4 QUICK
148(1)
5.3.4.5 FROMM
148(1)
5.3.5 High Resolution and Bounded Convective Schemes
148(1)
5.3.5.1 Normalized Variable Formulation
149(2)
5.3.5.2 Convective Boundedness Criteria
151(1)
5.3.5.3 High-Resolution Schemes
151(2)
5.3.5.4 The TVD Framework
153(3)
5.3.5.5 Implementation of Various Convective Schemes in Code
156(1)
5.4 Time-Dependent Methods
157(2)
5.4.1 One-Step Methods
158(1)
5.4.1.1 Forward Differencing (Euler Method)
158(1)
5.4.1.2 Backward Differencing (Backward Euler)
158(1)
5.4.1.3 Central Differencing (Crank-Nicolson)
158(1)
5.5 Time Discretization Methods Applied to the General Scalar Transport Equation
159(2)
5.5.1 Forward Differencing - Explicit Scheme
159(1)
5.5.2 Backward Differencing - Implicit Scheme
159(1)
5.5.3 Crank-Nicolson - Central Difference Scheme
160(1)
5.6 Courant Number
161(1)
5.7 Uses of Time-Marching in CFD
161(1)
5.8 Implementation of Boundary Conditions in Code
161(2)
5.8.1 Generalized Boundary Conditions
161(1)
5.8.2 Convective Boundary Conditions
162(1)
5.9 Examples
163(14)
5.10 Summary
177(2)
Questions
179(2)
Chapter 6 Solution of Incompressible Navier-Stokes Equations
181(26)
6.1 Introduction
181(1)
6.2 Pressure-Velocity Coupling
182(2)
6.3 The Vorticity-Stream Function Method
184(3)
6.3.1 Boundary Conditions
186(1)
6.4 Primitive Variable Methods
187(3)
6.4.1 Co-located Storage of Variables
187(2)
6.4.2 Staggered Grid
189(1)
6.5 Solution Methods for the Primitive Variable Form of N-S Equations
190(3)
6.5.1 The Artificial Compressibility Method
190(1)
6.5.2 The Pressure Correction Approach
191(1)
6.5.2.1 The MAC Method
192(1)
6.5.2.2 The Fractional Step Pressure Projection Method
192(1)
6.6 The SIMPLE Method
193(5)
6.6.1 Derivation of Velocity Correction and Pressure Correction Equations
193(1)
6.6.1.1 Pressure and Velocity Corrections
194(1)
6.6.2 Pressure Correction Equation
195(1)
6.6.3 The SIMPLE Algorithm
196(2)
6.7 Variants of SIMPLE
198(6)
6.7.1 The SIMPLER Algorithm
199(2)
6.7.2 The SIMPLEC Algorithm
201(1)
6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm
202(2)
6.8 Summary
204(1)
Questions
205(2)
Chapter 7 Finite Volume Method for Complex Geometries
207(46)
7.1 Introduction
207(1)
7.2 Staggered Grid Algorithm
207(1)
7.3 The Co-located Grid Algorithm
208(2)
7.4 Discretization Methods for Non-Orthogonal Structured Grids
210(7)
7.4.1 The Continuity Equation
211(1)
7.4.2 The Transport Equation
211(1)
7.4.2.1 Discretization of Convective Flux
212(2)
7.4.2.2 Discretization of Diffusive Flux
214(2)
7.4.2.3 Discretization of Pressure Term
216(1)
7.4.2.4 Implementation of the QUICK Scheme
216(1)
7.5 Solution of the Pressure Field
217(5)
7.5.1 Derivation of Pressure Correction and Velocity Correction Equations
217(2)
7.5.2 Implementation of Momentum Interpolation
219(3)
7.6 Extension to Three Dimension
222(9)
7.6.1 Discretization of Continuity Equations
223(1)
7.6.2 Discretization of Convective Flux
223(1)
7.6.3 Discretization of Diffusive Flux
224(3)
7.6.4 Discretization of the Pressure Term
227(1)
7.6.5 Implementation of the QUICK Scheme
227(1)
7.6.6 Implementation of the SIMPLE Algorithm
228(3)
7.7 Discretization Method for the Cartesian Structured Grid
231(9)
7.7.1 The Continuity Equation
231(2)
7.7.2 The Transport Equation
233(1)
7.7.2.1 Discretization of Convective Flux
233(1)
7.7.2.2 Discretization of Diffusive Flux
234(1)
7.7.2.3 Discretization of the Pressure Term
235(1)
7.7.2.4 Implementation of the QUICK Scheme
235(1)
7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation
236(2)
7.7.2.6 Implementation of the Momentum Interpolation
238(2)
7.8 Discretization Method for the Non-Orthogonal Unstructured Grid
240(5)
7.8.1 The Continuity Equation
240(1)
7.8.2 The Transport Equation
240(2)
7.8.2.1 Discretization of Convective Flux
242(1)
7.8.2.2 Discretization of Diffusive Flux
242(3)
7.8.2.3 Discretization of the Pressure Term
245(1)
7.9 Solution of the Pressure Field
245(5)
7.9.1 Derivation of Pressure Correction and Velocity Correction Equations
245(2)
7.9.2 Implementation of the Momentum Interpolation
247(2)
7.9.3 Implementation of Higher-Order Schemes
249(1)
7.10 Summary
250(1)
Questions
250(3)
Chapter 8 Solution of Algebraic Equations
253(26)
8.1 Introduction
253(1)
8.2 Direct Methods
253(5)
8.2.1 Gauss Elimination
253(2)
8.2.2 LU Decomposition
255(1)
8.2.3 Tri-Diagonal Matrix Algorithm
256(2)
8.3 Iterative Methods
258(4)
8.3.1 The Jacobi Method
258(1)
8.3.2 The Point Gauss-Seidel Method
259(1)
8.3.3 Point Successive Over-Relaxation Method
260(1)
8.3.4 The Line Gauss-Seidel Method
260(1)
8.3.5 Convergence of the Iterative Methods
261(1)
8.4 Conjugate Gradient (CG) Methods
262(2)
8.4.1 The Pre-Conditioned BCG Method
263(1)
8.4.2 The Pre-Conditioned CGS Method
263(1)
8.5 The Incomplete L-U Decomposition Method
264(4)
8.5.1 Introduction
264(1)
8.5.2 Pre-Conditioning by L-U Decomposition
265(3)
8.6 The Multigrid Method
268(4)
8.6.1 Coarsening Step
269(1)
8.6.2 Restriction Step
270(1)
8.6.3 Prolongation Step
270(1)
8.6.4 Cycling Strategy
271(1)
8.7 Examples
272(4)
8.8 Summary
276(1)
Questions
277(2)
Chapter 9 Turbulence Modeling
279(22)
9.1 Introduction
279(1)
9.2 What Is Turbulence?
279(1)
9.2.1 Characteristics of Turbulent Flows
279(1)
9.2.2 Task of Turbulence Modeling
280(1)
9.3 Direct Numerical Simulation (DNS)
280(1)
9.4 Reynolds Averaging
281(4)
9.4.1 Reynolds-Averaged Navier-Stokes (RANS) Equations
281(3)
9.4.2 Eddy Viscosity Models Hypothesis
284(1)
9.5 RANS Turbulence Models
285(10)
9.5.1 Zero-Equation Models
285(1)
9.5.1.1 Structure of the Turbulent Boundary Layer
286(1)
9.5.2 Key Modifications of Prandtl's Mixing Length Model
287(1)
9.5.2.1 The Cebaci-Smith Model
287(1)
9.5.2.2 The Baldwin-Lomax Model
288(1)
9.5.3 The Transport Equation for Turbulent Kinetic Energy (One-Equation Model)
288(1)
9.5.4 Two-Equation Models
289(1)
9.5.4.1 The Standard k-ε Model
290(1)
9.5.4.2 The Wilcox k-ω Model
290(1)
9.5.4.3 The SST k-ω (Menter) Turbulence Model
291(1)
9.5.4.4 Near-Wall Modifications for Two-Equation Models
292(3)
9.6 Reynolds Stress Transport (Equation-based) Models (RSTMs)
295(3)
9.7 Large Eddy Simulation
298(1)
9.8 Summary
298(1)
Questions
299(2)
Chapter 10 Grid Generation
301(22)
10.1 Introduction
301(1)
10.2 Geometry
301(1)
10.3 Grid Structure
301(2)
10.4 Classification of Grid Types
303(1)
10.5 Generating Structured Grids Fitting Complex Boundaries
304(2)
10.5.1 Blocking Out Cells
304(1)
10.5.2 Multi-Block Structured Grids
305(1)
10.5.3 Body-Fitted Grids
305(1)
10.6 Mesh Quality
306(1)
10.7 Adaptive Grid
307(1)
10.8 Grid-Generation Techniques
308(6)
10.8.1 Coordinate Transformation
308(2)
10.8.2 Grid Generation
310(1)
10.8.2.1 Algebraic Grid Generation
310(3)
10.8.2.2 Differential-Equation Based Techniques
313(1)
10.9 Unstructured Grid Generation
314(6)
10.9.1 Connectivity Information
315(1)
10.9.2 Triangular Grid Generation
316(1)
10.9.2.1 The Advancing-Front Technique
317(1)
10.9.2.2 The Delaunay-Based Method
318(2)
Questions
320(3)
Chapter 11 Best Practice Guidelines in CFD
323(12)
11.1 Introduction
323(1)
11.2 Sources of Error
323(2)
11.2.1 Model Errors and Uncertainties
324(1)
11.2.2 Discretization or Numerical Errors
324(1)
11.2.3 Iteration or Convergence Errors
324(1)
11.2.4 Round-off Errors
325(1)
11.2.5 Application Uncertainties
325(1)
11.2.6 User Errors
325(1)
11.2.7 Code Errors
325(1)
11.3 Best Practices Guidelines
325(6)
11.3.1 Geometry and Grid Design
325(1)
11.3.1.1 Geometry Generation
325(1)
11.3.1.2 Grid Design
326(1)
11.3.2 Discretization Schemes
326(1)
11.3.2.1 Spatial Discretization Errors
326(1)
11.3.2.2 Time Discretization Errors
326(1)
11.3.3 Convergence
327(1)
11.3.4 Modeling Uncertainty
327(1)
11.3.4.1 Solution Algorithms
327(1)
11.3.4.2 Turbulence Modeling
328(1)
11.3.4.3 Near-Wall Modeling
328(1)
11.3.5 Round-off Errors
329(1)
11.3.6 User Errors
329(1)
11.3.6.1 Boundary Conditions
329(2)
11.4 Analysis of Results, Sensitivity Studies and Uncertainties
331(1)
11.4.1 Analysis of Results
331(1)
11.4.2 Sensitivity Analysis
331(1)
11.4.3 Uncertainties
331(1)
11.5 Verification, Validation and Calibration
332(3)
11.5.1 Verification
332(1)
11.5.1.1 Code Verification
332(1)
11.5.1.2 Calculation Verification
332(1)
11.5.2 Validation
333(2)
Appendix 1 Area and Volume Calculation 335(8)
Appendix 2 Transformation of Governing Equations to Generalized Curvilinear Coordinates 343(6)
Appendix 3 Review of Vector Calculus 349(20)
Appendix 4 Case Studies 369(12)
References 381(6)
Index 387
D. G. Roychowdhury is currently working as executive director at the Sharda Group of Institutions, Agra, India. He received his Ph.D. from the Indian Institute of Technology, Madras,, India. Before joining the Sharda Group, he worked as Scientist at the Indira Gandhi Centre for Atomic Research, Kalpakkam, India; as a Research Associate at the University of Warwick, in England; and as Professor and Dean at the Hindustan Institute of Technology & Science, Chennai, India. His research areas include computational fluid dynamics, heat transfer, and thermal-hydraulic analysis of fast reactor core under normal and off-normal events. He has taught courses including thermodynamics, fluid mechanics, advanced fluid mechanics and computational fluid dynamics at undergraduate and graduate level. He has authored several research papers in peer reviewed journals.