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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

Library of Congress Record

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Hardback

 (ISBN-13: 9780521769693)

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Computational Fluid Dynamics
Cambridge University Press
9780521769693 - Computational Fluid Dynamics - By T. J. Chung
Index

Index

Accuracy 48–61, 187, 372

Acoustic intensity level 807

Additive Schwarz procedure 654–9

Adiabatic wall 206

Advancing front methods (AFM) 601–6

Atkin's algorithm 580

Albedo 876, 892

Algebraic grid generator 543–61, 579

Algebraic Reynolds stress model 702–3

Alternating direction implicit (ADI) 66, 72–3, 141, 173, 522

Amplification factor 70, 78

Approximate factorization 73–5, 141, 175

Arbitrary Lagrangian-Eulerian methods 912, 914, 930

Arc-length method 571

Arnoldi process 385

Arrhenius law 737

Artificial compressibility 106, 107, 126

Artificial viscosity (diffusion) 123–125, 127, 139, 140, 368, 371

Artificial viscosity flux limiters 195

Assembly of stiffness (diffusion, viscosity) matrix 212–5

Assembly of source vector 212–5

Axisymmetric ring elements 305, 306

Axisymmetric cylindrical heat conduction 335–6

Back scatter 707

Backward (upwind) differencing 7, 46

Baldwin-Lomax model 702–3

Banach space 256

Base functions

See interpolation functions

Beam-Warming method 85–6, 141, 156, 169–76, 524

Bernstein polynomials 581, 583

Beta spline 582, 583

Bezier curve 581–586

Bezier patches 583

BGK model 940, 941

Biharmonic equation 415

Black hole accretion 975–76

Boltzmann equation 940–941

Boolean matrix 246, 313

Boolean operators 609

Boundary and initial conditions 9, 17–24, 38–41, 197–207, 315–20, 347–55, 458–460

Dirichlet 17–20, 38–41

for Euler and Navier-Stokes system of equations 197–207

mixed, Robin 38–41

Neumann 9, 13–18, 20–24, 38–41, 347–354, 458–460

well-posedness 98, 201

Boundary element methods 245, 532–535

Bowyer algorithm 597–600

Box (tophat) function 707

Burger's Equation 87–90, 355, 402–404, 502

C0, C1, Cm continuity 307–308

Catmull-Rom form 582, 584

Cauchy/Robin boundary conditions 39, 317

Cebeci-Smith model 694

Cell area (Jacobian) method 570

Cell-centered average scheme 225–7

Cell-centered control volume 223–5

Central difference 6, 141, 371

CFL(Courant) number 77, 78, 368

Characteristic Galerkin method (CGM) 347, 445–6

Characteristic variables 134–5, 205

Chebyshev polynomials 473–5, 645, 776, 788, 931

Chemical equilibrium equations 714–54

Compatibility relations 132

Christoffel symbols 563, 574–7, 969, 1009–1016

Circum circle, circumradius, circumsphere 593–4

Clausius-Duhem inequality 437

Clustering function 553–5

Coarse grain parallelism 666

Combustion

See under chemically reactive flows

Completeness 307

Compressed sparse row 669

Compressibility condition 354

Compressibility effects 703–5

Compression corner flow 464

Condition number 256, 257

Conduction-radiation ratio 876, 906

Conforming elements 308

Conjugate gradient method (CGM) 337, 384

Consistency 61

Consistent mass matrix 359

Continuity across elements 307

Continuous space-time (CST) 327

Contravariant metric tensor 379, 440

Control functions 567, 579, 618–627

Control function 617–27

Control surfaces (volumes) 12–19, 219–32, 234–5, 501–9

Convection-diffusion equation 369

Convection-dominated flow 347–8

Convection Jacobians 131, 170, 181, 989–94

Convection matrix 355, 370

Convergence 62, 258, 259, 306–8

Convex hull 599

Coordinate transformation 94–8

Cost function 891

Couette flow 110

Coupled Eulerian-Langrangian methods 246, 535–8, 790

Courant (CFL) number 368, 372, 374

Covariant metric tensor 563

Crank-Nicolson scheme 71–5, 81, 108, 356, 362, 364

Cubic spline 535–7

Curl of three-dimensional vorticity transport equations 118, 417

Curvature tensor 574

Damköhler number 452, 743, 744, 784

Deflection angle 467

Delaunay-Voronoi methods (DVM) 591–600

Derivative finite difference operator 48

Diagonally dominant 113

Differential geometry 573–577

Differential operator 440

Diffusion gradient Jacobian 181, 433

Diffusion Jacobian 181, 989–994

Diffusion matrix (stiffness, viscosity) matrix 9, 355, 370

Diffusion number 68

Diffusion transport tensor 701

Diffusion velocity 738

Dilatation 353

Dilaunay triangulation 592–594

Direct numerical simulation 713–4, 792, 793, 796, 832, 931

Dirichlet boundary conditions 39, 315–17

Discontinuity-capturing diffusivity 454

Discontinuity-capturing factor 442

Discontinuity-capturing scheme (DCS) 376, 377, 439–43

Discontinuous Galerkin methods DGM) 347, 446–7

Discontinuous space-time (DST) 327, 377

Dispersion error 89

Dissipation error 79

Dissipation tensor 700

Dissociation 767, 779

Distributed shared memory 664–73

Domain decomposition methods 654–60

multiplicative Schwarz procedure 654–56

additive Schwarz procedure 660–1

parallel processing in 670, 677

Domain vertex methods 547–55

Double asymptotic approximation 373

Driven cavity flow 465–7

DuFort-Frankel methods 71, 522

Dulquist and Bjorck scheme 56

Dust infall 980–3

Eckert number 881

Eddy (turbulent) viscosity 710

Effectivity index 646

Eigenvalues 132, 143, 179, 204, 208

negative 204, 207

positive 204, 207

Eigenvectors 133, 134

Element-by-element (EBE) method 340, 381

Elliptic equations 31–3, 63–7, 98, 561, 572

Elliptic grid generator 561–8, 618

Emissive power 851–2

Energy dissipation range 708

Energy norm error 255, 630

Ensemble average 691

Entropy condition 151

Entropy controlled instability 839–44

Entropy mode acoustics 813–8

Entropy variables 437, 441–4

Entropy variable Jacobians 437, 438–40

Equation solvers 65, 76–77, 90–4, 337–42, 380–91

Gauss elimination 67

Gauss-Seidel iteration 65

generalized minimal residual (GMRES) method 380, 752

Jacobi iteration 65

Newton-Raphson method 380, 752

Runge-Kutta method 90, 168

Thomas algorithm 76

tridiagonal matrix algorithm (TDMA) 76

Equilibrium chemistry 744, 779

Error estimates 254–9, 645

Error coefficient vector 385

Error indicator 628–30, 645

Errors

iterative 65

round-off 65

sources of 91–94

truncation 46–62

Essentially nonoscillatory (ENO) schemes 163–5

Euler equations 129–166, 367–91

Eulerian differences 535

Explicit scheme 68–71, 77–81, 167, 365, 366

Extinction coefficient 853

Extrapolation methods 201

FDV parameters (variation parameters) 181–185, 448–59, 784

Ffowcs Williams-Hawkings equation 812, 836

Filtering functions 706

Fine grain parallelism 666

Finite difference operators 48–61

derivative 48

displacement 48

Finite element functions

trial functions, (base, interpolation, shape) 8, 262, 308

temporal test functions 254, 327

test functions 8, 377–9

Finite point methods 491–2

Finite rate chemistry 744, 777

First order variation parameters 183, 187

Flowfield-dependent variation methods 180–94, 448–67, 781, 828, 832, 923, 977–84

Fluid-particle mixture 923–7

Flux corrected transport (FCT) schemes 165–6

Flux extrapolation approximation 149

Flux implicit higher order accurate schemes 196

Flux vector splitting 142–5, 448

Forward differencing 7, 46

Fourier series 69

Fourier-cutoff function 707

Fractional step methods 75, 522

Frequency, fundamental 69

Front tracking methods 912

Froude number 978

Frozen chemistry 744

FTCS schemes 78, 81

FTFS schemes 77

Fully implicit continuous Eulerian (FICE) methods 956

Fundamental frequency 69

FVM via FDM 16, 216–39

FVM via FEM 17, 491–517

Galerkin methods 9, 243–54

characteristic (CGM) 426, 443–6

discontinuous (DGM) 243, 426, 446–8

generalized (GGM) 243, 347, 426, 435

generalized Petrov (GPG) 243, 347, 376–80, 426, 436–43

standard (SGM) 11, 243, 249, 309–24, 347, 912, 910

streamline diffusion Petrov (SUPG) 347, 374

Taylor (TGM) 243, 347, 426, 430–4, 777, 840

Galerkin test function 370, 377

Gather operation 669–70

Gauss elimination 67, 657

Gauss-Seidel iteration 65

Gaussian curvature 576

Gaussian quadrature 231, 292, 293, 484, 892, 909, 995–1002

Generalized Galerkin methods (GGM) 327–336, 430, 435

Generalized minimal residual (GMRES) 384–5, 752

Generalized Taylor-Galerkin methods 243, 426, 430–4, 510, 530

Generalized Petrov-Galerkin methods 374, 377, 378, 410, 531

Gibbs function 752

Givens Householder rotation matrix 386, 390

Godunov method 145–8, 155

Gram-Schmidt orthogonalization 385

Granularity in parallel processing 673

Gravitation 965

Gravitational source term Jacobian 1009–1016

Green's function 532

Grid clustering 553–555

Grid generation

structured 591–615

unstructured 543–587

Hanging nodes 630–631, 637–638

Heat conduction 98, 99, 335

Helmholtz equation 533, 808

Hermite polynomial 271, 581

Hermite polynomial elements 271–3, 544

Hessenberg matrix 385, 387, 395

Hexahedral element 303–5, 608

Hilbert space 255, 629

hp methods 645–9

hr methods 640–3

Hyperbolic equations 31–3, 77–81, 93, 332–4, 522

Hyperbolic grid generator 565–71

Hypersonic flows 120, 467 769–75

Ill-conditioned 257

Implicit scheme 71–72, 81, 90, 169, 331, 356, 365, 366

Incompressibility condition 106–15

Incompressible limit 178, 439

Inertial subrange 708

Inner product 8, 218, 249, 369

Insertion polygon 594

Interpolation functions 8, 247, 262, 308, 472, 543

Intrinsic time scale 440

Ionization 767, 772

Isoparametric element 286–297, 477–80, 909

Iterative error 65

Iterative paving method 613

Jacobi iteration 65

Jacobi preconditioner 382

Jacobians

convection flux 131, 170, 989

diffusion flux 989

diffusion gradient 181, 425, 979–84

source term 1003, 1014

K – ε model 696–7, 781, 785, 932

K – ω model 698

Kerr black hole geometry 669

Kirchhoff's law 853

Kirchhoff's method 809–10, 821, 823

Kolmogorov microscale 455, 708

Krylov space 385

Laasonen method 71, 522

Lagrange multipliers 318, 320, 753, 754

Lagrange polynomial elements 269–71, 543–4, 580

Lagrangian differences 537

Lanczos algorithm 382, 383, 385

Landau-Teller model 773

Laplace equations 63, 561–3

Large eddy simulation 706–733, 792, 794

Law of mass action 736–7

Lax-Friedrichs scheme 138

Lax method 80, 83, 151

Lax-Wendroff method 80, 82, 83, 105, 138, 523, 525

LBB Condition 325, 408

Leapfrog method 80, 168, 363

Midpoint 87

Least square methods 488–490, 890–2

Legendre polynomials 466–7, 645

Legendre spectral mode functions 479, 470, 645

Leonard stress 707

Level set methods 912

Lighthill's acoustic energy 811

Load balancing 674–5

Dynamic 675

Static 674, 675

Local and global approaches for FEM 309, 310, 311

Local remeshing 642

L2 norm error 256, 385, 464

Lumped mass matrix 359–60

MacCormack scheme 82, 85, 89, 98, 105, 140, 168, 525, 820

Mach number 29, 120, 455, 838, 845

Mach wave 20, 30

Magnetohydrodynamics 937–9

Marker and cell (MAC) 106, 115, 409

Mass (Favre) average 691–2

Mass fraction 736

Mass matrix

Consistent 359

Lumped 359–360

Matrix-by-vector product 669

Matrix norm 256

Maxwell equations 932–9

Mesh enrichment (p) methods 644

Mesh movement (r) methods 639–40

Mesh refinement (h) methods 628–39

Mesh parameter 258

Mesh smoothing 604, 605

Meshless methods

See finite point methods

MIMD, SIMD 666–8

Minimizer error vector 385

Minkowski coordinate transformation 972–3

Mixed methods 325, 326, 407

Mixed/Robin boundary conditions 38–41

Molar concentration 736

Mole fraction 736

Monotonicity condition 152

Monte Carlo methods 538–9

Multiblock structured grids 587–9

Multigrid methods 661–666

restriction process 661–5

prolongation process 661–5

Multiplicative Schwarz procedure 654–60

Multi-step method 81

Multitasking 673

Multithreading 672, 673, 678–83

MUSCL approach 148–50

Natural coordinates 267, 278, 282

Navier-Stokes system of equations 33–8, 166–214, 426–460

Neumann boundary conditions 9, 13–18, 20–24, 38–41, 97, 310, 312, 317–20, 508

Newton-Raphson method 380, 382, 751, 752, 799, 891, 896

Nonreflecting boundary conditions 204–5

Node-centered control volume 219–23

Noise control 827–832

Normed adjusted error 385

Normed error vector 385

Number density 736

Numerical diffusion 357, 358

Numerical diffusion test function 367–80

Numerical diffusion factor 368–73

Numerical diffusion matrix 358, 370

Numerical diffusion test functions 368–9, 370, 379, 441

Numerical viscosity 153, 371

Nusselt number 904

Operator splitting 411, 777

Operator splitting methods 411, 412

Optical thickness 865, 909

Optically thick 871–85

Optically thin 869–83

Optimal control methods 490, 889, 890–2, 904

Optimality condition 647, 847

Orr-Sommerfeld equation 419, 421

Orthogonality 8, 249, 623

Outscatter 707

Over-relaxation method 66, 99, 128

Pade' scheme 60

Parabolic equations 31–3, 67–73, 327–32

Parabolic grid generator 572

Parallel processing 666–75

Partial pressure 736

Particle-in-cell (PIC) 119, 228, 538

PDE mapping methods 561–572

Peclet number 183, 370, 453, 743, 881

Penalty methods 326, 408

Petrov-Galerkin (integral) methods 368, 370, 374

Petrov-Galerkin test function 377

Phase angle 70

Phase field formulation 912

Phase interaction methods 922, 932

PISO 106, 112–14, 175–7, 509, 528

Planck's law 851

Plasma processing 946–56

Point implicit method 197, 777

Pointwise error 256

Poisson equations 115, 572, 655

Potential equation 121–9

Prandtl mixing length model 693

Prandtl number 909

Preconditioned conjugate gradient 382

Preconditioning 178–9, 396, 438, 657

Predictor-corrector 81–3, 140, 168

Pressure-correction method 108, 409, 410

Pressure mode acoustics 808–810

Pressure-strain correlation tensor 701

Primitive variables 132, 442–6

Primitive variable Jacobian 438, 439

Principal curvature 578

Prism element 302, 303

Probability density function 758–61, 785, 793

Projection method 249

Prolongation process 661–5

Pure convection 399–402

QR algorithm 421

Quadrilateral elements 286–297

Quadtree and octree methods 614

Radiative transfer equation 873

Ramjet combuster 779

Rarefied gas dynamics 941–946

Reflection wave (reflection boundary) 205

Ristriction process 661–665

Reconstruction function 163

Relativistic hydrodynamics 976–7

Relativistic shock tube 974–5

Relativity

general 965–72

special 965

Reynolds number 107, 184, 370, 428, 488, 909, 931

Reynolds average Navier-Stokes (RANS) 704, 706, 928

Reynolds stress 455, 707

Reynolds stress model 700–702, 780

Richardson method 71

Riemann-Christoffel tensor 576

Riemann invariants 135

Roe's approximate Riemann solver 146

Root mean square error 256

Rossland approximation 871

Rotational difference 125

Round-off errors 65

Runge-Kutta method 90, 168, 776, 792

Scatter operation 669–70

Scattering media 890

Schur complement matrix 656

Schwarzschild metric 969

Scramjet combustion 731–735

Second order variation parameters 183, 187

Semiconductor plasma processing 946–56

Semi-implicit pressure correction 413, 413

Sensible enthalpy 734, 740, 741

Shock angle 467

Shape functions

See interpolation functions

Shear layer 206

Shock-capturing mechanism 189–90

Shock tube problems 465, 974, 975

Shock wave 120, 205

Shock wave boundary layer flow 463–6

SIMPLE, SIMPLER, SIMPLEC 106, 111, 118, 528

Singularity 648

Slivers 594

Small perturbation approximations 33, 121

Sobolev space 255

Sound wave 29

Smooth particle hydrodynamics (SPH) 491, 492, 913

Smoothness 623

Solar corona mass ejection 956–7

Solid angle 853

Sound pressure level 807

Space-time

continuous 327

discontinuous 327–35

Space-time Galerkin/least squares 378

Spatial average 691

Spectral element methods 472–87, 788

Spectral methods 472

Speedup factor 666

Speed of light 965

Speed of sound 29

Splitting methods 81

Spray combustion 746–8, 786, 791

Stability and accuracy 369–375

Stability conditions

Numerical 61, 70, 233, 234, 369–75

Physical 421, 839–47

Stephan-Boltzmann law 842

Spray combustion 746–8, 786–91

Stiffness (diffusion or viscosity) matrix 9, 251, 277, 309–17

Stoichiometric condition 736

Stoke's flow 324–7

Stream function 39, 115

Streamline diffusion in GLS 439

Streamline diffusion in GPG 439

Streamline diffusion method (SDM) 243, 367

Streamline upwind Petrov-Galerkin (SUPG) 347, 374

Subgrid scale model 709

Subgrid stress tensor 707

Subsonic flow 39, 120, 123

Supersonic flow 30, 120, 128

Surface grid generator 572–9, 584–7

Surface tension 352, 1014–21

Surface tension force Jacobian 1003–8

Surface traction 353

Sutherland's law 34, 429

Taylor-Galerkin methods (TGM) 355, 366, 777, 840

Taylor series 83, 85, 86, 180, 356, 368, 430, 449

Temporal parameter 329

Temporal test functions 254–327

Tensor notation (index notation) 246

Test function

spatial 8, 247, 262, 308

temporal 328, 435, 472

Tetrahedral elements 298

Thomas algorithm 76

Threaded parallel program 678–83

Three plus one formulation 967–8

Time average 690–1

Total variation diminishing (TVD) schemes 150–62, 189, 526, 527

Transfinite interpolation (TFI) methods 555–60

Transient problems 327

Transonic flow 120, 123

Trial function 8, 247, 262, 308, 470

Triangular elements 273, 286

Triangular prism elements 302, 303

Tridiagonal matrix algorithm (TDMA) 76

Truncation errors 46–62

Two-phase flows 352, 912–934

Two-step explicit scheme 358, 359

Two-temperature model 772, 801

Unstable waves 839–45, 846, 847

Upwind scheme 124, 526

First order 142–50

Second order 150–62, 448

Unstructured finite element mesh refinements 650–2

Unstructured grid generation 591–615

Variable extrapolation approach 148

Variational equation 8, 250, 319

Variational functional 622

Variational methods 249, 251, 377, 622–7

Variation parameters (FDV parameters) 181–5, 448–59

Variational principles 243, 251

Vector pipelines 666

Vibration model 772–3, 799

View factors 858–62

Viscosity (diffusion, stiffness ) matrix 9, 251, 277, 309–17

Volume-of-fluid methods 912–21

Volume tracking methods 912

Von Neumann stability analysis 68–71, 77–80

Vortex methods 115–118, 414–20

Voronoi polygons 592–4

Vorticity mode acoustics 811–3

Vorticity transport equation 117

Wall functions 698–9

Watson algorithm 592–7

Wave equation 87

Wave number 9, 51, 253

Weak form (solution) 9, 369

Weight function 621

Weighted residual methods 249, 252, 472–99

Well-conditioned 257, 438, 439

Well-posedness 198, 201




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