Index

eqn symbol, 1, 2
eqn symbol, 3, 4
eqn symbol, 5
eqn symbol, 6, 7
eqn symbol, 8
1D, 9, 10
2D, 11
3D, 12, 13, 14, 15, 16, 17, 18

adiabatic, 19
advection, 20
    bounded scheme, 21
    derivative, 22
    discretisation, 23, 24, 25, 26
    interpolation, 27
    limited linear scheme, 28
    limited schemes, 29
    linear upwind, 30, 31
    minmod scheme, 32
    TVD schemes, 33, 34
    upwind scheme, 35
    van Albada scheme, 36
    van Leer scheme, 37
adverse pressure gradient, 38, 39
aerodynamics
    automotive, 40
    of a cylinder, 41
algebraic multi-grid, 42
algorithm
    PIMPLE, 43
    PISO, 44
    SIMPLE, 45
anisotropic, 46
area of a triangle, 47
aspect ratio, 48, 49
asymptotic consistency, 50
axisymmetry condition, 51

backward time scheme, 52
Bernoulli equation, 53
biconjugate gradient, 54
body force, 55, 56, 57
boundary
    face data, 58
    mesh, 59
boundary condition
    axisymmetric, 60
    body force, 61
    direction mixed, 62
    Dirichlet, 63
    entrainment, 64
    examples, 65
    factors, 66, 67, 68
    fixed gradient, 69
    fixed value, 70
    free, 71
    freestream, 72, 73
    fundamentals, 74
    heat flux, 75, 76, 77
    heat transfer coefficient, 78
    inlet, 79
    , 80
    eqn, 81
    eqn, 82
    inlet-outlet, 83
    inlet-outlet-velocity, 84
    mixed, 85
    momentum flux, 86
    Neumann, 87
    no-slip, 88
    nonuniform velocity, 89
    numerical framework, 90
    outlet, 91
    pressure inlet, 92
    recommendations, 93
    Robin, 94
    supersonic, 95
    symmetry, 96
    total pressure, 97
    transform, 98
    turbulence fields, 99
    wall, 100
    wall function, 101
boundary layer, 102
    buffer layer, 103
    inertial sub-layer, 104
    laminar, 105
    one-seventh power law, 106, 107
    separation, 108
    thermal, 109
    thickness, 110
    turbulent, 111
    viscous sub-layer, 112
boundedness, 113
buffer layer, 114
building a CFD simulation, 115
bulk viscosity, 116
buoyancy, 117

CAD, 118, 119
calorically perfect gas, 120
capturing physics, 121
Cartesian axes, 122
cavity, 123
cell
    aspect ratio, 124, 125, 126
    centre, 127
    splitting, 128
centre
    of a cell, 129
    of a triangle, 130
CFD, see computational fluid dynamics
CFL, 132
circulation, 133
commutative, 134
computational
    cost, 135
    fluid dynamics, 136
computer aided design, see CAD
conductivity, 138
conjugate gradient
    in practice, 139
    method, 140
    summary, 141
conservation, 142
    equations, 143
    of angular momentum, 144
    of energy, 145
    of internal energy, 146
    of mass, 147
    of momentum, 148
    of turbulent kinetic energy, 149
control volumes, 150
controls
    momentum predictor, 151
    non-orthogonal correctors, 152
convection, see advection
    natural, 154
convergence, 155
    steady-state, 156
Courant
    -Friedrichs-Lewy, see CFL
    number, 158
Crank-Nicolson, 159
curl
    derivative, 160
    discretisation, 161
cylinder, 162

decoupled equations, 163
deformation, 164
    tensor, 165
degree of freedom, 166
Delaunay triangulation, 167
density, 168, 169
descent methods, 170
design process, 171
deviatoric tensor, 172
diagonal
    dominance, 173, 174
    equality, 175
diffusion, 176, 177
dimensionless number
    Courant, 178
    drag coefficient, 179
    Euler, 180
    Froude, 181
    Knudsen, 182
    lift coefficient, 183
    Mach, 184
    Péclet, 185, 186
    Prandtl, 187, 188, 189
    Reynolds, 190, 191, 192
    Schmidt, 193
    Strouhal, 194, 195
direct methods, 196
direction mixed condition, 197
Dirichlet condition, 198
discharge coefficient, 199
discretisation, 200
    0/1 bounded, 201
    advection, 202
    calculated derivatives, 203
    curl, 204
    explicit linear term, 205
    general divergence, 206
    gradient, 207
    implicit linear term, 208
    Laplacian, 209
    linear interpolation, 210, 211
    lower/upper bounded, 212
    mag-square grad-grad, 213
    multi-dimensional, 214
    multiple components, 215
    multivariate, 216
    non-orthogonal correction, 217
    of equations, 218
    other terms, 219, 220
    overview, 221
    recommended schemes, 222
    surface normal gradient, 223
    time, 224
    upwind interpolation, 225
distributive, 226
disturbance
    propagation of, 227
divergence, 228
    discretisation, 229
    of a tensor, 230
    of a vector, 231
    of stress, 232
downwind, 233
drag coefficient, 234
dynamic viscosity, 235

eddy
    size, 236
    viscosity, 237
energy
    and temperature, 238
    cascade, 239
    conservation, 240
    internal, 241, 242
    kinetic, 243
    reference, 244
    solving for, 245
ensemble average, 246
entrainment, 247
equation
    advection-diffusion, 248
    pressure, 249
    summary, 250
    systems of, 251
    under-relaxation, 252
equipartition theorem, 253
error, 254
Euler
    number, 255
    time scheme, 256
explicit, 257, 258, 259, 260
extensive properties, 261
external flow, 262
extrapolation, 263

face
    area vector, 264, 265, 266
    centre, 267, 268
    non-orthogonality, 269
    unit vector, 270
far-field, 271, 272
favourable
    pressure gradient, 273
field
    pressure, 274
    scalar, 275
    temperature, 276
    tensor, 277
    under-relaxation, 278
    vector, 279
    velocity, 280
finite volume, 281, 282
    concept, 283
    mesh, 284
    overview, 285
five-thirds law, 286
fixed
    gradient condition, 287
    value condition, 288
flow
    around a cylinder, 289
    around a vehicle, 290
    circulation, 291
    external, 292, 293
    in a volume, 294
    incompressible, 295
    internal, 296
    recirculation, 297
    through a surface, 298
fluid
    dynamics, 299
    Newtonian, 300
    Stokesian, 301
flux, 302, 303
    boundary condition, 304
    corrector, 305, 306, 307
    of heat, 308, 309
    of mass, 310
force
    at a surface, 311
    body, 312, 313, 314
    buoyancy, 315
    on a body, 316
free decay of turbulence, 317
friction velocity, 318
Froude number, 319

GAMG, 320
    agglomeration, 321
    method, 322
    summary, 323
gas
    calorically perfect, 324
    constant, 325
    diatomic, 326
    ideal, 327
    monatomic, 328
    thermally perfect, 329
    universal constant, 330
Gauss’s theorem, 331, 332, 333, 334, 335
Gauss-Seidel
    convergence, 336
    method, 337
    summary, 338
    symmetric method, 339
Gaussian elimination, 340
governing equations, 341
gradient, 342
    boundary factor, 343, 344, 345
    discretisation, 346, 347, 348
    internal factor, 349, 350, 351
    least squares, 352
    limiting, 353
    of pressure, 354
    point linear scheme, 355
    surface normal, 356, 357

heat
    capacity, 358
    conduction, 359
    flux, 360, 361
    of formation, 362
    source, 363
    transfer coefficient, 364
    transfer in a room, 365

ideal gas, 366
identity tensor, 367
implicit, 368, 369, 370, 371, 372
incompressible flow, 373
inertial sub-layer, 374
inlet, 375
    nonuniform velocity, 376
inner product
    of two tensors, 377
    of two vectors, 378
integral
    over a volume/surface, 379
intensive properties, 380
internal energy, 381
interpolation, 382
    cell-face, 383
    downwind, 384
    for advection, 385
    linear, 386, 387
    point linear, 388
    skewness correction, 389
    upwind, 390
    weights, 391
isotropic, 392, 393
iterative, 394
    methods, 395

k model, 396
    algorithm, 397
    coefficients, 398
    initialisation, 399
    Jones-Launder, 400
    Launder-Sharma, 401
    low-eqn, 402
    near-wall damping, 403
eqn model, 404
    “standard” 2006, 405
    cross-diffusion, 406
    enhancements, 407
    SST, 408
    stress limiter, 409
Kármán
    constant, 410
    vortex street, 411, 412
kinematic
    pressure, 413
    viscosity, 414
kinetic
    theory, 415
    turbulent energy, 416
Knudsen number, 417
Kolmogorov
    five-thirds law, 418
    scales, 419, 420

laminar, 421
Laplacian, 422, 423
    corrected scheme, 424, 425
    discretisation, 426, 427, 428
    orthogonal scheme, 429
least squares gradient, 430
lift coefficient, 431
linear
    interpolation, 432, 433
    upwind, 434
local time-stepping, 435
log law
    for temperature, 436
    for velocity, 437
logarithmic law of the wall, see log law
low-eqn turbulence model, 439

Mach number, 440
mass
    conservation, 441
    density, 442, 443
    flux, 444
    molar, 445
matrix
    building example, 446
    coefficients, 447, 448
    construction, 449
    convergence, 450
    diagonal dominance, 451, 452, 453
    extensive, 454
    operations, 455
    positive-definite, 456
    preconditioning, 457
    size, 458
    solution convergence, 459
    solution residual, 460
    sparse, 461, 462
    structure, 463
    symmetry, 464
    under-relaxation, 465
matrix solvers
    biconjugate gradient, 466
    conjugate gradient, 467
    Gauss-Seidel, 468
    multi-grid, 469
    steepest descent, 470
    summary, 471
    symmetric Gauss-Seidel, 472
mesh, 473
    aspect ratio, 474, 475
    block-structured, 476
    boundary, 477
    data, 478
    finite volume, 479
    generation, 480
    non-orthogonality, 481
    polyhedral, 482
    refinement, 483
    renumbering, 484
    skewness, 485
    unstructured, 486
minimisation problem, 487
mixed boundary condition, 488
mixing
    length, 489, 490
    turbulent, 491
molar mass, 492
momentum
    conservation, 493
    corrector, 494, 495, 496
    matrix, 497
    predictor, 498
momentum corrector, 499
multi-grid
    algebraic, 500
    method, 501

nabla operator, 502
natural convection, 503
Neumann condition, 504
Newton-Raphson method, 505
Newtonian fluid, 506
non-orthogonal, 507, 508
numerical diffusion, 509

one-dimensional, see 1D
orthogonal, 511
    tensor, 512
outer product, 513
outlet, 514

Péclet number, 515, 516
patch, 517
    deltas, 518
    geometric data, 519
persistence of velocities, 520
PIMPLE algorithm, 521
PISO
    algorithm, 522
    momentum predictor, 523
    non-orthogonal correctors, 524
    summary, 525
positive-definite, 526
power
    mechanical, 527
    source, 528
Prandtl
    number, 529, 530, 531
    one-seventh power law, 532
    turbulent number, 533
pressure, 534
    adverse gradient, 535, 536
    at a wall, 537
    equation, 538, 539, 540, 541
    favourable gradient, 542
    field, 543
    fixing, 544
    gradient, 545
    kinematic, 546, 547
    kinetic theory, 548
    velocity coupling, 549
prototype simulation, 550

quadratic form, 551

realisations, 552
reference
    energy, 553
    temperature, 554
region of influence, 555, 556
renumbering a mesh, 557
residual, 558
    calculation at intervals, 559
Reynolds
    averaged simulation, 560
    experiment, 561
    number, 562, 563, 564
    stress, 565, 566
Richardson poem, 567
Robin boundary condition, 568
rotation
    of a fluid element, 569
    tensor, 570
roughness, 571

scalar field, 572
scale similarity, 573
scales of turbulence, 574
Schmidt number, 575
second order time scheme, 576
segregated solution, 577
shear
    parallel, 578
    pure, 579
SIMPLE
    algorithm, 580
    convergence, 581
    residual control, 582
    summary, 583, 584
skew tensor, 585
skewness, 586, 587
    correction, 588
solution
    iterative, 589
    overview, 590
    pseudo-transient, 591
    stability, 592
    steady-state, 593
    transient, 594
    transient controls, 595
source vector, 596
sparse matrix, 597
specific heat capacity, 598
spherical tensor, 599
spin tensor, 600, 601
steady-state
    convergence, 602
    solution, 603
steepest descent, 604
Stokes theorem, 605
Stokesian fluid, 606
stress, 607
    divergence, 608
    tensor, 609
    turbulent shear, 610
Strouhal number, 611, 612
surface
    area vector, 613
    force, 614
    integral, 615
    normal gradient, 616
    roughness, 617
Sweby diagram, 618
symmetric tensor, 619
symmetry
    boundary condition, 620
    of a matrix, 621

tanks and tubes, 622
Taylor’s series, 623, 624
temperature, 625
    and energy, 626
    field, 627
    reference, 628
    scale, 629
    to energy conversion, 630
tensor, 631
    algebra, 632
    deforation, 633
    deviatoric, 634
    double inner product, 635
    field, 636
    identity, 637
    inner product, 638
    orthogonal, 639
    rank, 640, 641
    rotation, 642, 643
    skew, 644
    spherical, 645
    spin, 646, 647
    stress, 648, 649
    symmetric, 650
    trace, 651
    transformation, 652, 653
thermal
    boundary layer, 654
    conductivity, 655, 656
    mass, 657
thermally
    perfect gas, 658
thermodynamics, 659
three-dimensional, see 3D
time derivative, 661, 662
    local rate of change, 663
    material, 664, 665
time discretisation, 666, 667, 668
time scheme
    backward, 669
    Crank-Nicolson, 670
    Euler, 671
    first order, 672
    second order, 673
tolerance
    absolute, 674
    relative, 675
    setting, 676
traction vector, 677
transform condition, 678
transient solution, 679
transport equation, 680
    temperature, 681
    vorticity, 682
turbulence
    boundary conditions, 683
    cost of simulating, 684
    direct numerical simulation, 685
    energy cascade, 686
    free decay, 687
    generation, 688
    in a pipe, 689
    inlet, 690
    k model, 691
    large-eddy simulation, 692
    modelling summary, 693
    near walls, 694
    overview, 695
    picture of, 696
    Reynolds stress, 697
    Reynolds-averaged simulation, 698
    scales of, 699
    summary, 700
    transition, 701
    transport of , 702
    transport of eqn, 703
    viscous sub-layer, 704
    wall function, 705
turbulent, 706
    boundary layer, 707
    dissipation rate, 708, 709
    heat transfer, 710
    intensity, 711, 712
    kinetic energy, 713, 714
    mixing, 715, 716
    mixing length, 717, 718, 719
    shear stress, 720
    specific dissipation rate, 721
    thermal conductivity, 722
    viscosity, 723
two-dimensional, see 2D

under-relaxation, 725
    coefficients, 726
unit vector, 727
universal gas constant, 728
upwind, 729, 730
    accuracy, 731
    boundedness, 732
    numerical diffusion, 733

value
    boundary factor, 734, 735, 736
    internal factor, 737, 738, 739
vector, 740
    addition, 741
    algebra, 742
    curl, 743
    field, 744
    identities, 745
    inner product, 746
    magnitude, 747
    outer product, 748
    scalar division, 749
    scalar multiplication, 750
    subtraction, 751
    traction, 752
    unit, 753, 754
velocity, 755
    at a wall, 756
    field, 757
    friction, 758
    translational, 759
Venturi tube, 760
viscosity
    bulk, 761
    dynamic, 762
    eddy, 763
    kinematic, 764
    nature of, 765
    of common fluids, 766
viscous sub-layer, 767
volume
    integral, 768
    of a cell, 769
vortex
    ring, 770
    stretching, 771
vorticity, 772
    generation, 773
    transport, 774

wall boundary condition, 775
wall function, 776
    alternative, 777
    continuous, 778
    rough, 779
    standard, 780
    thermal, 781
    turbulence fields, 782
wedge boundary condition, 783
weights, 784

Notes on CFD: General Principles - Index