Index
symbol, 3, 4
symbol, 5
symbol, 6, 7
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
, 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
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
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
,
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