Notes on Computational Fluid Dynamics: General Principles

symbol, 1, 2

symbol, 3, 4

symbol, 5

symbol, 6, 7

symbol, 8

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
    , 81
    , 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

model, 396
    algorithm, 397
    coefficients, 398
    initialisation, 399
    Jones-Launder, 400
    Launder-Sharma, 401
    low-, 402
    near-wall damping, 403
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- 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