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Computational Fluid Dynamics
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  • 349 b/w illus. 28 tables 32 exercises
  • Page extent: 1058 pages
  • Size: 253 x 215 mm
  • Weight: 2.11 kg

Library of Congress

  • Dewey number: 532/.050285
  • Dewey version: 22
  • LC Classification: QA911 .C476 2010
  • LC Subject headings:
    • Fluid dynamics--Data processing

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 (ISBN-13: 9780521769693)

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Computational Fluid Dynamics
Cambridge University Press
9780521769693 - Computational Fluid Dynamics - By T. J. Chung
Table of Contents

Contents

Preface to the First Edition
xix
Preface to the Revised Second Edition
xxii
Part One.     Preliminaries
1             Introduction
3
1.1           General
3
1.1.1         Historical Background
3
1.1.2         Organization of Text
4
1.2           One-Dimensional Computations by Finite Difference Methods
6
1.3           One-Dimensional Computations by Finite Element Methods
7
1.4           One-Dimensional Computations by Finite Volume Methods
11
1.4.1         FVM via FDM
11
1.4.2         FVM via FEM
13
1.5           Neumann Boundary Conditions
13
1.5.1         FDM
14
1.5.2         FEM
15
1.5.3         FVM via FDM
15
1.5.4         FVM via FEM
16
1.6           Example Problems
17
1.6.1         Dirichlet Boundary Conditions
17
1.6.2         Neumann Boundary Conditions
20
1.7           Summary
24
References
26
2             Governing Equations
29
2.1           Classification of Partial Differential Equations
29
2.2           Navier-Stokes System of Equations
33
2.3           Boundary Conditions
38
2.4           Summary
41
References
42
Part Two.     Finite Difference Methods
3             Derivation of Finite Difference Equations
45
3.1           Simple Methods
45
3.2           General Methods
46
3.3           Higher Order Derivatives
50
3.4           Multidimensional Finite Difference Formulas
53
3.5           Mixed Derivatives
57
3.6           Nonuniform Mesh
59
3.7           Higher Order Accuracy Schemes
60
3.8           Accuracy of Finite Difference Solutions
61
3.9           Summary
62
References
62
4             Solution Methods of Finite Difference Equations
63
4.1           Elliptic Equations
63
4.1.1         Finite Difference Formulations
63
4.1.2         Iterative Solution Methods
65
4.1.3         Direct Method with Gaussian Elimination
67
4.2           Parabolic Equations
67
4.2.1         Explicit Schemes and von Neumann Stability Analysis
68
4.2.2         Implicit Schemes
71
4.2.3         Alternating Direction Implicit (ADI) Schemes
72
4.2.4         Approximate Factorization
73
4.2.5         Fractional Step Methods
75
4.2.6         Three Dimensions
75
4.2.7         Direct Method with Tridiagonal Matrix Algorithm
76
4.3           Hyperbolic Equations
77
4.3.1         Explicit Schemes and Von Neumann Stability Analysis
77
4.3.2         Implicit Schemes
81
4.3.3         Multistep (Splitting, Predictor-Corrector) Methods
81
4.3.4         Nonlinear Problems
83
4.3.5         Second Order One-Dimensional Wave Equations
87
4.4           Burgers' Equation
87
4.4.1         Explicit and Implicit Schemes
88
4.4.2         Runge-Kutta Method
90
4.5           Algebraic Equation Solvers and Sources of Errors
91
4.5.1         Solution Methods
91
4.5.2         Evaluation of Sources of Errors
91
4.6           Coordinate Transformation for Arbitrary Geometries
94
4.6.1         Determination of Jacobians and Transformed Equations
94
4.6.2         Application of Neumann Boundary Conditions
97
4.6.3         Solution by MacCormack Method
98
4.7           Example Problems
98
4.7.1         Elliptic Equation (Heat Conduction)
98
4.7.2         Parabolic Equation (Couette Flow)
100
4.7.3         Hyperbolic Equation (First Order Wave Equation)
101
4.7.4         Hyperbolic Equation (Second Order Wave Equation)
103
4.7.5         Nonlinear Wave Equation
104
4.8           Summary
105
References
105
5             Incompressible Viscous Flows via Finite Difference Methods
106
5.1           General
106
5.2           Artificial Compressibility Method
107
5.3           Pressure Correction Methods
108
5.3.1         Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
108
5.3.2         Pressure Implicit with Splitting of Operators
112
5.3.3         Marker-and-Cell (MAC) Method
115
5.4           Vortex Methods
115
5.5           Summary
118
References
119
6             Compressible Flows via Finite Difference Methods
120
6.1           Potential Equation
121
6.1.1         Governing Equations
121
6.1.2         Subsonic Potential Flows
123
6.1.3         Transonic Potential Flows
123
6.2           Euler Equations
129
6.2.1         Mathematical Properties of Euler Equations
130
6.2.1.1       Quasilinearization of Euler Equations
130
6.2.1.2       Eigenvalues and Compatibility Relations
132
6.2.1.3       Characteristic Variables
134
6.2.2         Central Schemes with Combined Space-Time Discretization
136
6.2.2.1       Lax-Friedrichs First Order Scheme
138
6.2.2.2       Lax-Wendroff Second Order Scheme
138
6.2.2.3       Lax-Wendroff Method with Artificial Viscosity
139
6.2.2.4       Explicit MacCormack Method
140
6.2.3         Central Schemes with Independent Space-Time Discretization
141
6.2.4         First Order Upwind Schemes
142
6.2.4.1       Flux Vector Splitting Method
142
6.2.4.2       Godunov Methods
145
6.2.5         Second Order Upwind Schemes with Low Resolution
148
6.2.6         Second Order Upwind Schemes with High Resolution (TVD Schemes)
150
6.2.7         Essentially Nonoscillatory Scheme
163
6.2.8         Flux-Corrected Transport Schemes
165
6.3           Navier-Stokes System of Equations
166
6.3.1         Explicit Schemes
167
6.3.2         Implicit Schemes
169
6.3.3         PISO Scheme for Compressible Flows
175
6.4           Preconditioning Process for Compressible and Incompressible Flows
178
6.4.1         General
178
6.4.2         Preconditioning Matrix
179
6.5           Flowfield-Dependent Variation Methods
180
6.5.1         Basic Theory
180
6.5.2         Flowfield-Dependent Variation Parameters
183
6.5.3         FDV Equations
185
6.5.4         Interpretation of Flowfield-Dependent Variation Parameters
187
6.5.5         Shock-Capturing Mechanism
188
6.5.6         Transitions and Interactions between Compressible and Incompressible Flows
191
6.5.7         Transitions and Interactions between Laminar and Turbulent Flows
193
6.6           Other Methods
195
6.6.1         Artificial Viscosity Flux Limiters
195
6.6.2         Fully Implicit High Order Accurate Schemes
196
6.6.3         Point Implicit Methods
197
6.7           Boundary Conditions
197
6.7.1         Euler Equations
197
6.7.1.1       One-Dimensional Boundary Conditions
197
6.7.1.2       Multi-Dimensional Boundary Conditions
204
6.7.1.3       Nonreflecting Boundary Conditions
204
6.7.2         Navier-Stokes System of Equations
205
6.8           Example Problems
207
6.8.1         Solution of Euler Equations
207
6.8.2         Triple Shock Wave Boundary Layer Interactions Using FDV Theory
208
6.9           Summary
213
References
214
7             Finite Volume Methods via Finite Difference Methods
218
7.1           General
218
7.2           Two-Dimensional Problems
219
7.2.1         Node-Centered Control Volume
219
7.2.2         Cell-Centered Control Volume
223
7.2.3         Cell-Centered Average Scheme
225
7.3           Three-Dimensional Problems
227
7.3.1         3-D Geometry Data Structure
227
7.3.2         Three-Dimensional FVM Equations
232
7.4           FVM-FDV Formulation
234
7.5           Example Problems
239
7.6           Summary
239
References
239
Part Three.   Finite Element Methods
8             Introduction to Finite Element Methods
243
8.1           General
243
8.2           Finite Element Formulations
245
8.3           Definitions of Errors
254
8.4           Summary
259
References
260
9             Finite Element Interpolation Functions
262
9.1           General
262
9.2           One-Dimensional Elements
264
9.2.1         Conventional Elements
264
9.2.2         Lagrange Polynomial Elements
269
9.2.3         Hermite Polynomial Elements
271
9.3           Two-Dimensional Elements
273
9.3.1         Triangular Elements
273
9.3.2         Rectangular Elements
284
9.3.3         Quadrilateral Isoparametric Elements
286
9.4           Three-Dimensional Elements
298
9.4.1         Tetrahedral Elements
298
9.4.2         Triangular Prism Elements
302
9.4.3         Hexahedral Isoparametric Elements
303
9.5           Axisymmetric Ring Elements
305
9.6           Lagrange and Hermite Families and Convergence Criteria
306
9.7           Summary
308
References
308
10            Linear Problems
309
10.1          Steady-State Problems – Standard Galerkin Methods
309
10.1.1        Two-Dimensional Elliptic Equations
309
10.1.2        Boundary Conditions in Two Dimensions
315
10.1.3        Solution Procedure
320
10.1.4        Stokes Flow Problems
324
10.2          Transient Problems – Generalized Galerkin Methods
327
10.2.1        Parabolic Equations
327
10.2.2        Hyperbolic Equations
332
10.2.3        Multivariable Problems
334
10.2.4        Axisymmetric Transient Heat Conduction
335
10.3          Solutions of Finite Element Equations
337
10.3.1        Conjugate Gradient Methods (CGM)
337
10.3.2        Element-by-Element (EBE) Solutions of FEM Equations
340
10.4          Example Problems
342
10.4.1        Solution of Poisson Equation with Isoparametric Elements
342
10.4.2        Parabolic Partial Differential Equation in Two Dimensions
343
10.5          Summary
346
References
346
11            Nonlinear Problems/Convection-Dominated Flows
347
11.1          Boundary and Initial Conditions
347
11.1.1        Incompressible Flows
348
11.1.2        Compressible Flows
353
11.2          Generalized Galerkin Methods and Taylor-Galerkin Methods
355
11.2.1        Linearized Burgers' Equations
355
11.2.2        Two-Step Explicit Scheme
358
11.2.3        Relationship between FEM and FDM
362
11.2.4        Conversion of Implicit Scheme into Explicit Scheme
365
11.2.5        Taylor-Galerkin Methods for Nonlinear Burgers' Equations
366
11.3          Numerical Diffusion Test Functions
367
11.3.1        Derivation of Numerical Diffusion Test Functions
368
11.3.2        Stability and Accuracy of Numerical Diffusion Test Functions
369
11.3.3        Discontinuity-Capturing Scheme
376
11.4          Generalized Petrov-Galerkin (GPG) Methods
377
11.4.1        Generalized Petrov-Galerkin Methods for Unsteady Problems
377
11.4.2        Space-Time Galerkin/Least Squares Methods
378
11.5          Solutions of Nonlinear and Time-Dependent Equations and Element-by-Element Approach
380
11.5.1        Newton-Raphson Methods
380
11.5.2        Element-by-Element Solution Scheme for Nonlinear Time Dependent FEM Equations
381
11.5.3        Generalized Minimal Residual Algorithm
384
11.5.4        Combined GPE-EBE-GMRES Process
391
11.5.5        Preconditioning for EBE-GMRES
396
11.6          Example Problems
399
11.6.1        Nonlinear Wave Equation (Convection Equation)
399
11.6.2        Pure Convection in Two Dimensions
399
11.6.3        Solution of 2-D Burgers' Equation
402
11.7          Summary
402
References
404
12            Incompressible Viscous Flows via Finite Element Methods
407
12.1          Primitive Variable Methods
407
12.1.1        Mixed Methods
407
12.1.2        Penalty Methods
408
12.1.3        Pressure Correction Methods
409
12.1.4        Generalized Petrov-Galerkin Methods
410
12.1.5        Operator Splitting Methods
411
12.1.6        Semi-Implicit Pressure Correction
413
12.2          Vortex Methods
414
12.2.1        Three-Dimensional Analysis
415
12.2.2        Two-Dimensional Analysis
418
12.2.3        Physical Instability in Two-Dimensional Incompressible Flows
419
12.3          Example Problems
421
12.4          Summary
424
References
424
13            Compressible Flows via Finite Element Methods
426
13.1          Governing Equations
426
13.2          Taylor-Galerkin Methods and Generalized Galerkin Methods
430
13.2.1        Taylor-Galerkin Methods
430
13.2.2        Taylor-Galerkin Methods with Operator Splitting
433
13.2.3        Generalized Galerkin Methods
435
13.3          Generalized Petrov-Galerkin Methods
436
13.3.1        Navier-Stokes System of Equations in Various Variable Forms
436
13.3.2        The GPG with Conservation Variables
439
13.3.3        The GPG with Entropy Variables
441
13.3.4        The GPG with Primitive Variables
442
13.4          Characteristic Galerkin Methods
443
13.5          Discontinuous Galerkin Methods or Combined FEM/FDM/FVM Methods
446
13.6          Flowfield-Dependent Variation Methods
448
13.6.1        Basic Formulation
448
13.6.2        Interpretation of FDV Parameters Associated with Jacobians
451
13.6.3        Numerical Diffusion
453
13.6.4        Transitions and Interactions between Compressible and Incompressible Flows and between Laminar and Turbulent Flows
454
13.6.5        Finite Element Formulation of FDV Equations
455
13.6.6        Boundary Conditions
458
13.7          Example Problems
460
13.8          Summary
469
References
469
14            Miscellaneous Weighted Residual Methods
472
14.1          Spectral Element Methods
472
14.1.1        Spectral Functions
473
14.1.2        Spectral Element Formulations by Legendre Polynomials
477
14.1.3        Two-Dimensional Problems
481
14.1.4        Three-Dimensional Problems
485
14.2          Least Squares Methods
488
14.2.1        LSM Formulation for the Navier-Stokes System of Equations
488
14.2.2        FDV-LSM Formulation
489
14.2.3        Optimal Control Method
490
14.3          Finite Point Method (FPM)
491
14.4          Example Problems
493
14.4.1        Sharp Fin Induced Shock Wave Boundary Layer Interactions
493
14.4.2        Asymmetric Double Fin Induced Shock Wave Boundary Layer Interaction
496
14.5          Summary
499
References
499
15            Finite Volume Methods via Finite Element Methods
501
15.1          General
501
15.2          Formulations of Finite Volume Equations
502
15.2.1        Burgers' Equations
502
15.2.2        Incompressible and Compressible Flows
510
15.2.3        Three-Dimensional Problems
512
15.3          Example Problems
513
15.4          Summary
517
References
518
16            Relationships between Finite Differences and Finite Elements and Other Methods
519
16.1          Simple Comparisons between FDM and FEM
520
16.2          Relationships between FDM and FDV
524
16.3          Relationships between FEM and FDV
528
16.4          Other Methods
532
16.4.1        Boundary Element Methods
532
16.4.2        Coupled Eulerian-Lagrangian Methods
535
16.4.3        Particle-in-Cell (PIC) Method
538
16.4.4        Monte Carlo Methods (MCM)
538
16.5          Summary
540
References
540
Part Four.    Automatic Grid Generation, Adaptive Methods, And Computing Techniques
17            Structured Grid Generation
543
17.1          Algebraic Methods
543
17.1.1        Unidirectional Interpolation
543
17.1.2        Multidirectional Interpolation
547
17.1.2.1      Domain Vertex Method
547
17.1.2.2      Transfinite Interpolation Methods (TFI)
555
17.2          PDE Mapping Methods
561
17.2.1        Elliptic Grid Generator
561
17.2.1.1      Derivation of Governing Equations
561
17.2.1.2      Control Functions
567
17.2.2        Hyperbolic Grid Generator
568
17.2.2.1      Cell Area (Jacobian) Method
570
17.2.2.2      Arc-Length Method
571
17.2.3        Parabolic Grid Generator
572
17.3          Surface Grid Generation
572
17.3.1        Elliptic PDE Methods
572
17.3.1.1      Differential Geometry
573
17.3.1.2      Surface Grid Generation
577
17.3.2        Algebraic Methods
579
17.3.2.1      Points and Curves
579
17.3.2.2      Elementary and Global Surfaces
583
17.3.2.3      Surface Mesh Generation
584
17.4          Multiblock Structured Grid Generation
587
17.5          Summary
590
References
590
18            Unstructured Grid Generation
591
18.1          Delaunay-Voronoi Methods
591
18.1.1        Watson Algorithm
592
18.1.2        Bowyer Algorithm
597
18.1.3        Automatic Point Generation Scheme
600
18.2          Advancing Front Methods
601
18.3          Combined DVM and AFM
606
18.4          Three-Dimensional Applications
607
18.4.1        DVM in 3-D
607
18.4.2        AFM in 3-D
608
18.4.3        Curved Surface Grid Generation
609
18.4.4        Example Problems
609
18.5          Other Approaches
610
18.5.1        AFM Modified for Quadrilaterals
611
18.5.2        Iterative Paving Method
613
18.5.3        Quadtree and Octree Method
614
18.6          Summary
615
References
615
19            Adaptive Methods
617
19.1          Structured Adaptive Methods
617
19.1.1        Control Function Methods
617
19.1.1.1      Basic Theory
617
19.1.1.2      Weight Functions in One Dimension
619
19.1.1.3      Weight Function in Multidimensions
621
19.1.2        Variational Methods
622
19.1.2.1      Variational Formulation
622
19.1.2.2      Smoothness Orthogonality and Concentration
623
19.1.3        Multiblock Adaptive Structured Grid Generation
627
19.2          Unstructured Adaptive Methods
627
19.2.1        Mesh Refinement Methods (h-Methods)
628
19.2.1.1      Error Indicators
628
19.2.1.2      Two-Dimensional Quadrilateral Element
630
19.2.1.3      Three-Dimensional Hexahedral Element
634
19.2.2        Mesh Movement Methods (r-Methods)
639
19.2.3        Combined Mesh Refinement and Mesh Movement Methods (hr-Methods)
640
19.2.4        Mesh Enrichment Methods (p-Method)
644
19.2.5        Combined Mesh Refinement and Mesh Enrichment Methods (hp-Methods)
645
19.2.6        Unstructured Finite Difference Mesh Refinements
650
19.3          Summary
652
References
652
20            Computing Techniques
654
20.1          Domain Decomposition Methods
654
20.1.1        Multiplicative Schwarz Procedure
655
20.1.2        Additive Schwarz Procedure
660
20.2          Multigrid Methods
661
20.2.1        General
661
20.2.2        Multigrid Solution Procedure on Structured Grids
661
20.2.3        Multigrid Solution Procedure on Unstructured Grids
665
20.3          Parallel Processing
666
20.3.1        General
666
20.3.2        Development of Parallel Algorithms
667
20.3.3        Parallel Processing with Domain Decomposition and Multigrid Methods
671
20.3.4        Load Balancing
674
20.4          Example Problems
676
20.4.1        Solution of Poisson Equation with Domain Decomposition Parallel Processing
676
20.4.2        Solution of Navier-Stokes System of Equations with Multithreading
678
20.5          Summary
683
References
684
Part Five.    Applications
21            Applications to Turbulence
689
21.1          General
689
21.2          Governing Equations
690
21.3          Turbulence Models
693
21.3.1        Zero-Equation Models
693
21.3.2        One-Equation Models
696
21.3.3        Two-Equation Models
696
21.3.4        Second Order Closure Models (Reynolds Stress Models)
700
21.3.5        Algebraic Reynolds Stress Models
702
21.3.6        Compressibility Effects
703
21.4          Large Eddy Simulation
706
21.4.1        Filtering, Subgrid Scale Stresses, and Energy Spectra
706
21.4.2        The LES Governing Equations for Compressible Flows
709
21.4.3        Subgrid Scale Modeling
709
21.5          Direct Numerical Simulation
713
21.5.1        General
713
21.5.2        Various Approaches to DNS
714
21.6          Solution Methods and Initial and Boundary Conditions
715
21.7          Applications
716
21.7.1        Turbulence Models for Reynolds Averaged Navier-Stokes (RANS)
716
21.7.2        Large Eddy Simulation (LES)
718
21.7.3        Direct Numerical Simulation (DNS) for Compressible Flows
726
21.8          Summary
728
References
731
22            Applications to Chemically Reactive Flows and Combustion
734
22.1          General
734
22.2          Governing Equations in Reactive Flows
735
22.2.1        Conservation of Mass for Mixture and Chemical Species
735
22.2.2        Conservation of Momentum
739
22.2.3        Conservation of Energy
740
22.2.4        Conservation Form of Navier-Stokes System of Equations in Reactive Flows
742
22.2.5        Two-Phase Reactive Flows (Spray Combustion)
746
22.2.6        Boundary and Initial Conditions
748
22.3          Chemical Equilibrium Computations
750
22.3.1        Solution Methods of Stiff Chemical Equilibrium Equations
750
22.3.2        Applications to Chemical Kinetics Calculations
754
22.4          Chemistry-Turbulence Interaction Models
755
22.4.1        Favre-Averaged Diffusion Flames
755
22.4.2        Probability Density Functions
758
22.4.3        Modeling for Energy and Species Equations in Reactive Flows
763
22.4.4        SGS Combustion Models for LES
764
22.5          Hypersonic Reactive Flows
766
22.5.1        General
766
22.5.2        Vibrational and Electronic Energy in Nonequilibrium
768
22.6          Example Problems
775
22.6.1        Supersonic Inviscid Reactive Flows (Premixed Hydrogen-Air)
775
22.6.2        Turbulent Reactive Flow Analysis with Various RANS Models
780
22.6.3        PDF Models for Turbulent Diffusion Combustion Analysis
785
22.6.4        Spectral Element Method for Spatially Developing Mixing Layer
788
22.6.5        Spray Combustion Analysis with Eulerian-Lagrangian Formulation
788
22.6.6        LES and DNS Analyses for Turbulent Reactive Flows
792
22.6.7        Hypersonic Nonequilibrium Reactive Flows with Vibrational and Electronic Energies
798
22.7          Summary
802
References
802
23            Applications to Acoustics
806
23.1          Introduction
806
23.2          Pressure Mode Acoustics
808
23.2.1        Basic Equations
808
23.2.2        Kirchhoff's Method with Stationary Surfaces
809
23.2.3        Kirchhoff's Method with Subsonic Surfaces
810
23.2.4        Kirchhoff's Method with Supersonic Surfaces
810
23.3          Vorticity Mode Acoustics
811
23.3.1        Lighthill's Acoustic Analogy
811
23.3.2        F{fowcs} Williams-Hawkings Equation
812
23.4          Entropy Mode Acoustics
813
23.4.1        Entropy Energy Governing Equations
813
23.4.2        Entropy Controlled Instability (ECI) Analysis
814
23.4.3        Unstable Entropy Waves
816
23.5          Example Problems
818
23.5.1        Pressure Mode Acoustics
818
23.5.2        Vorticity Mode Acoustics
832
23.5.3        Entropy Mode Acoustics
839
23.6          Summary
847
References
848
24            Applications to} Combined Mode Radiative Heat Transfer
851
24.1          General
851
24.2          Radiative Heat Transfer
855
24.2.1        Diffuse Interchange in an Enclosure
855
24.2.2        View Factors
858
24.2.3        Radiative Heat Flux and Radiative Transfer Equation
865
24.2.4        Solution Methods for Integrodifferential Radiative Heat Transfer Equation
873
24.3          Radiative Heat Transfer in Combined Modes
874
24.3.1        Combined Conduction and Radiation
874
24.3.2        Combined Conduction, Convection, and Radiation
881
24.3.3        Three-Dimensional Radiative Heat Flux Integral Formulation
892
24.4          Example Problems
896
24.4.1        Nonparticipating Media
896
24.4.2        Solution of Radiative Heat Transfer Equation in Nonparticipating Media
898
24.4.3        Participating Media with Conduction and Radiation
902
24.4.4        Participating Media with Conduction, Convection, and Radiation
902
24.4.5        Three-Dimensional Radiative Heat Flux Integration Formulation
906
24.5          Summary
910
References
910
25            Applications to Multiphase Flows
912
25.1          General
912
25.2          Volume of Fluid Formulation with Continuum Surface Force
914
25.2.1        Navier-Stokes System of Equations
914
25.2.2        Surface Tension
916
25.2.3        Surface and Volume Forces
918
25.2.4        Implementation of Volume Force
920
25.2.5        Computational Strategies
921
25.3          Fluid-Particle Mixture Flows
923
25.3.1        Laminar Flows in Fluid-Particle Mixture with Rigid Body Motions of Solids
923
25.3.2        Turbulent Flows in Fluid-Particle Mixture
926
25.3.3        Reactive Turbulent Flows in Fluid-Particle Mixture
927
25.4          Example Problems
930
25.4.1        Laminar Flows in Fluid-Particle Mixture
930
25.4.2        Turbulent Flows in Fluid-Particle Mixture
931
25.4.3        Reactive Turbulent Flows in Fluid-Particle Mixture
932
25.5          Summary
934
References
934
26            Applications to Electromagnetic Flows
937
26.1          Magnetohydrodynamics
937
26.2          Rarefied Gas Dynamics
941
26.2.1        Basic Equations
941
26.2.2        Finite Element Solution of Boltzmann Equation
943
26.3          Semiconductor Plasma Processing
946
26.3.1        Introduction
946
26.3.2        Charged Particle Kinetics in Plasma Discharge
949
26.3.3        Discharge Modeling with Moment Equations
953
26.3.4        Reactor Model for Chemical Vapor Deposition (CVD) Gas Flow
955
26.4          Applications
956
26.4.1        Applications to Magnetohydrodynamic Flows in Corona Mass Ejection
956
26.4.2        Applications to Plasma Processing in Semiconductors
957
26.5          Summary
962
References
963
27            Applications to Relativistic Astrophysical Flows
965
27.1          General
965
27.2          Governing Equations in Relativistic Fluid Dynamics
966
27.2.1        Relativistic Hydrodynamics Equations in Ideal Flows
966
27.2.2        Relativistic Hydrodynamics Equations in Nonideal Flows
968
27.2.3        Pseudo-Newtonian Approximations with Gravitational Effects
973
27.3          Example Problems
974
27.3.1        Relativistic Shock Tube
974
27.3.2        Black Hole Accretion
975
27.3.3        Three-Dimensional Relativistic Hydrodynamics
976
27.3.4        Flowfield Dependent Variation (FDV) Method for Relativistic Astrophysical Flows
977
27.4          Summary
983
References
984
Appendixes
987
A             Three-Dimensional Flux Jacobians
989
B             Gaussian Quadrature
995
C             Two Phase Flow – Source Term Jacobians for Surface Tension
1003
D             Relativistic Astrophysical Flow Metrics, Christoffel Symbols, and FDV Flux and Source Term Jacobians
1009
E             Homework Problems
1017
Index
1029



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