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E-raamat: Computational Fluid Dynamics: Incompressible Turbulent Flows

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 01-Oct-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319453040
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Computational Fluid Dynamics: Incompressible Turbulent FlowsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 01-Oct-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319453040
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This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.

Numerical simulation of fluid flow.- Finite-difference discretization of the advection-diffusion equation.- Numerical simulation of incompressible flows.- Incompressible flow solver for generalized coordinate system.- Immersed boundary methods.- Numerical simulation of turbulent flows.- Reynolds-averaged Navier-Stokes equations.- Large-eddy simulation.- Appendix A: Generalized coordinate system.- Appendix B: Fourier analysis of flow field.- Appendix C: Modal decomposition methods.
1 Numerical Simulation of Fluid Flows
1(22)
1.1 Introduction
1(1)
1.2 Overview of Fluid Flow Simulations
2(2)
1.3 Governing Equations of Fluid Flows
4(10)
1.3.1 Conservation Laws
4(2)
1.3.2 Closure of the Governing Equations
6(1)
1.3.3 Divergence and Gradient Forms
7(2)
1.3.4 Indicial Notation
9(1)
1.3.5 Governing Equations of Incompressible Flow
10(3)
1.3.6 Properties of Partial Differential Equations
13(1)
1.4 Grids for Simulating Fluid Flows
14(3)
1.5 Discretization Methods
17(1)
1.6 Verification and Validation
18(1)
1.7 Remarks
19(1)
1.8 Exercises
20(3)
References
21(2)
2 Finite-Difference Discretization of the Advection-Diffusion Equation
23(50)
2.1 Introduction
23(1)
2.2 Advection-Diffusion Equation
24(1)
2.3 Finite-Difference Approximation
25(22)
2.3.1 Taylor Series Expansion
26(6)
2.3.2 Polynomial Approximation
32(3)
2.3.3 Central Difference at Midpoints
35(1)
2.3.4 Compatibility of Finite Differencing
36(2)
2.3.5 Spatial Resolution
38(4)
2.3.6 Behavior of Discretization Error
42(5)
2.4 Time Stepping Methods
47(4)
2.4.1 Single-Step Methods
47(3)
2.4.2 Multi-Step Methods
50(1)
2.5 Stability Analysis
51(14)
2.5.1 Stability of Time Stepping Methods
52(2)
2.5.2 von Neumann Analysis
54(1)
2.5.3 Stability of the Discrete Advection Equation
55(2)
2.5.4 Stability of the Discrete Diffusion Equation
57(2)
2.5.5 Stability of the Discrete Advection-Diffusion Equation
59(3)
2.5.6 Time Step Constraints for Advection and Diffusion
62(2)
2.5.7 Amplitude and Phase Errors
64(1)
2.6 Higher-Order Finite Difference
65(2)
2.7 Consistency of Finite-Difference Methods
67(1)
2.8 Remarks
68(1)
2.9 Exercises
69(4)
References
72(1)
3 Numerical Simulation of Incompressible Flows
73(74)
3.1 Introduction
73(1)
3.2 Time Stepping for Incompressible Flow Solvers
73(3)
3.3 Incompressible Flow Solvers
76(11)
3.3.1 Fractional-Step (Projection) Method
77(1)
3.3.2 Simplified MAC (SMAC) Method
78(1)
3.3.3 Highly Simplified MAC (HSMAC) Method and Semi-Implicit Method for Pressure Linked Equation (SIMPLE)
79(1)
3.3.4 Accuracy and Stability of Time Stepping
80(2)
3.3.5 Summary of Time Stepping for Incompressible Flow Solvers
82(5)
3.4 Spatial Discretization of Pressure Gradient Term
87(13)
3.4.1 Pressure Poisson Equation
87(5)
3.4.2 Iterative Method for the Pressure Poisson Equation
92(7)
3.4.3 Iterative Method for HSMAC Method
99(1)
3.5 Spatial Discretization of Advection Term
100(14)
3.5.1 Compatibility and Conservation
101(6)
3.5.2 Discretization on Nonuniform Grids
107(3)
3.5.3 Upwinding Schemes
110(4)
3.6 Spatial Discretization of Viscous Term
114(4)
3.7 Summary of the Staggered Grid Solver
118(2)
3.8 Boundary and Initial Conditions
120(16)
3.8.1 Boundary Setup
120(3)
3.8.2 Solid Wall Boundary Condition
123(5)
3.8.3 Inflow and Outflow Boundary Conditions
128(5)
3.8.4 Far-Field Boundary Condition
133(2)
3.8.5 Initial Condition
135(1)
3.9 High-Order Accurate Spatial Discretization
136(5)
3.9.1 High-Order Accurate Finite Difference
136(1)
3.9.2 Compatibility of High-Order Finite Differencing of Advective Term
137(2)
3.9.3 Boundary Conditions for High-Order Accurate Schemes
139(2)
3.10 Remarks
141(1)
3.11 Exercises
141(6)
References
144(3)
4 Incompressible Flow Solvers for Generalized Coordinate System
147(32)
4.1 Introduction
147(1)
4.2 Selection of Basic Variables
148(2)
4.3 Strong Conservation Form of the Governing Equations
150(3)
4.3.1 Strong Conservation Form
150(1)
4.3.2 Mass Conservation
151(1)
4.3.3 Momentum Conservation
151(2)
4.4 Basic Variables and Coordinate System
153(4)
4.5 Incompressible Flow Solvers Using Collocated Grids
157(3)
4.6 Spatial Discretization of Pressure Gradient Term
160(6)
4.6.1 Pressure Gradient Term
160(3)
4.6.2 Pressure Poisson Equation
163(2)
4.6.3 Iterative Solver for the Pressure Poisson Equation
165(1)
4.7 Spatial Discretization of Advection Term
166(4)
4.7.1 Compatibility and Conservation
166(2)
4.7.2 Upwinding Schemes
168(2)
4.8 Spatial Discretization of Viscous Term
170(1)
4.9 Boundary Conditions
170(2)
4.10 High-Order Accurate Spatial Discretization
172(1)
4.11 Evaluation of Coordinate Transform Coefficients
173(2)
4.12 Remarks
175(1)
4.13 Exercises
176(3)
References
177(2)
5 Immersed Boundary Methods
179(28)
5.1 Introduction
179(1)
5.2 Continuous Forcing Approach
180(13)
5.2.1 Discrete Delta Functions
182(6)
5.2.2 Original Immersed Boundary Method
188(2)
5.2.3 Immersed Boundary Projection Method
190(3)
5.3 Discrete Forcing Approach
193(5)
5.3.1 Direct Forcing Method
193(1)
5.3.2 Consistent Direct Forcing Method
194(3)
5.3.3 Cut-Cell Immersed Boundary Method
197(1)
5.4 Applications of Immersed Boundary Methods
198(3)
5.4.1 Flow Around a Circular Cylinder
199(1)
5.4.2 Turbulent Flow Through a Nuclear Rod Bundle
199(2)
5.5 Remarks
201(1)
5.6 Exercises
202(5)
References
204(3)
6 Numerical Simulation of Turbulent Flows
207(30)
6.1 Introduction
207(1)
6.2 Direct Numerical Simulation of Turbulent Flows
208(10)
6.2.1 Reynolds Number
208(2)
6.2.2 Full Turbulence Simulation
210(2)
6.2.3 Direct Numerical Simulation of Turbulence
212(1)
6.2.4 Turbulence Simulation with Low Grid Resolution
213(5)
6.3 Representation of Turbulent Flows
218(13)
6.3.1 Turbulence Models
218(2)
6.3.2 Governing Equations for Turbulent Flow
220(1)
6.3.3 Turbulence Modeling Approaches
221(1)
6.3.4 Visualization of Vortical Structures
222(3)
6.3.5 Coherent Structure Function
225(1)
6.3.6 Rotational Invariance
226(1)
6.3.7 Modal Decomposition of Turbulent Flows
227(4)
6.4 Remarks
231(1)
6.5 Exercises
232(5)
References
233(4)
7 Reynolds-Averaged Navier--Stokes Equations
237(32)
7.1 Introduction
237(1)
7.2 Reynolds-Averaged Equations
237(4)
7.2.1 Reynolds Average
237(2)
7.2.2 Reynolds Stress Equation
239(2)
7.3 Modeling of Eddy Viscosity
241(5)
7.4 k--ε Model
246(10)
7.4.1 Treatment of Near-Wall Region
249(3)
7.4.2 Computational Details of the k--ε Model
252(2)
7.4.3 Features and Applications of the k--ε Model
254(2)
7.5 Other Eddy-Viscosity Models
256(3)
7.6 Reynolds Stress Equation Model
259(4)
7.6.1 Basic Form of the Stress Equation
259(4)
7.6.2 Features of the Stress Equation Model
263(1)
7.7 Remarks
263(2)
7.8 Exercises
265(4)
References
267(2)
8 Large-Eddy Simulation
269(40)
8.1 Introduction
269(1)
8.2 Governing Equations for LES
269(7)
8.2.1 Filtering
270(4)
8.2.2 Governing Equations for Large-Eddy Simulation
274(2)
8.3 Smagorinsky Model
276(6)
8.3.1 Local Equilibrium and Eddy-Viscosity Assumptions
276(1)
8.3.2 Derivation of the Smagorinsky Model
277(1)
8.3.3 Properties of the Smagorinsky Model
278(1)
8.3.4 Modification in the Near-Wall Region
279(3)
8.4 Scale-Similarity Model
282(2)
8.4.1 Bardina Model
282(1)
8.4.2 Mixed Model
283(1)
8.5 Dynamic Model
284(5)
8.5.1 Dynamic Eddy-Viscosity Model
285(3)
8.5.2 Extensions of the Dynamic Model
288(1)
8.6 Other SGS Eddy-Viscosity Models
289(5)
8.6.1 Structure Function Model
289(1)
8.6.2 Coherent Structure Model
290(2)
8.6.3 One-Equation SGS Model
292(2)
8.7 Numerical Methods for Large-Eddy Simulation
294(9)
8.7.1 Computation of SGS Eddy Viscosity
294(3)
8.7.2 Implementation of Filtering
297(3)
8.7.3 Boundary and Initial Conditions
300(2)
8.7.4 Influence of Numerical Accuracy
302(1)
8.8 Remarks
303(2)
8.9 Exercises
305(4)
References
306(3)
Appendix A Generalized Coordinate System 309(16)
Appendix B Fourier Analysis of Flow Fields 325(14)
Appendix C Modal Decomposition Methods 339(14)
Index 353
Dr. Takeo Kajishima is Professor of Mechanical Engineering at Osaka University.  He holds B.Eng., M.Eng., and D.Eng. degrees from Osaka University in Mechanical Engineering.  His areas of expertise include simulation and modeling of multiphase flows, turbulent flows, and flow-structure interaction on the basis of computational fluid dynamics. He is a fellow of the Japan Society of Mechanical Engineering and the Japan Society of Fluid Mechanics.





Dr. Kunihiko Taira is Assistant Professor of Mechanical Engineering at Florida State University.  He received his B.S. degree in Aerospace Engineering with a double major in Mathematics from the University of Tennessee, Knoxville and his M.S. and Ph.D. degrees in Mechanical Engineering from California Institute of Technology.  His research interests are in the areas of computational fluid dynamics, unsteady flows, active flow control, and reduced-order models.
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