Characteristics finite element methods in computational fluid dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Schriftenreihe: | Computational fluid and solid mechanics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 711 - 725 |
| Beschreibung: | XXV, 727 S. Ill., graph. Darst. |
| ISBN: | 9783540251811 3540251812 |
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| 100 | 1 | |a Iannelli, Joe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Characteristics finite element methods in computational fluid dynamics |c Joe Iannelli |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XXV, 727 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Computational fluid and solid mechanics | |
| 500 | |a Literaturverz. S. 711 - 725 | ||
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 0 | 7 | |a Numerische Strömungssimulation |0 (DE-588)4690080-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Numerische Strömungssimulation |0 (DE-588)4690080-9 |D s |
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| 856 | 4 | |u http://catdir.loc.gov/catdir/enhancements/fy0818/2006925962-d.html |3 Beschreibung für Leser | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015036571&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1812898693798428672 |
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| adam_text |
JOE IANNELLI
CHARACTERISTIC
S FINITE
ELEMENT METHOD
S
IN COMPUTATIONA
L FLUID
DYNAMIC
S
WITH 384 FIGURES
Q SPRINGER
CONTENTS
PREFAC
E VI
I
A BRIE
F HISTOR
Y O
F THEORETICA
L AN
D COMPUTATIONA
L FLUI
D DYNAMIC
S XXII
I
1 GOVERNIN
G EQUATION
S O
F FLUI
D MECHANIC
S 1
1.1 FLUI
D PARTICL
E 1
1.2 MATHEMATICA
L DESCRIPTIO
N OF FLUI
D FLOW 4
1.3 TRANSPOR
T THEORE
M 8
1.3.1 SURFACE INTEGRA
L FOR
M 9
1.3.2 DIVERGENCE FORM 11
1.4 FLOWING AN
D STATIONAR
Y FLUI
D VOLUMES 13
1.5 STRESS TENSOR 13
1.5.1 GEOMETR
Y OF A TETRAHEDRO
N 13
1.5.2 SURFACE TRACTIO
N 15
1.5.3 STRES
S TENSOR SYMMETR
Y 16
1.5.4 NORMA
L STRESSES 17
1.5.5 STRESS INVARIANT
, MECHANICAL PRESSUR
E AN
D DEVIATORIC STRESSES 18
1.6 FLOW STAT
E VARIABLES 19
1.7 FUNDAMENTA
L EQUATION
S 20
1.7.1 CONSERVATION OF MASS: TH
E CONTINUIT
Y EQUATIO
N 20
1.7.2 SECOND LAW OF MECHANICS: TH
E LINEAR MOMENTU
M EQUATIO
N 21
1.7.3 TH
E FIRS
T LAW OF THERMODYNAMICS
: TH
E TOTA
L ENERG
Y EQUATIO
N .
. 23
1.8 CONSEQUENCES OF MASS CONSERVATIO
N 26
1.8.1 SUBSTANTIV
E DERIVATIVE 26
1.8.2 SUBSTANTIVE-DERIVATIV
E FORM OF TH
E TRANSPOR
T THEORE
M 27
1.8.3 INTERCHANG
E OF DIFFERENTIATION ORDE
R FOR MASS AN
D TIM
E 27
1.9 VELOCITY DIVERGENCE 28
1.9.1 PHYSICA
L SIGNIFICANCE 28
1.9.2 EQUATION
S FOR A FLUI
D PARTICL
E 28
1.10 ENERG
Y EQUATION
S 29
1.10.1 KINETI
C ENERG
Y EQUATIO
N 30
1.10.2 RIGID-MOTION AN
D DEFORMATION WORK 31
1.10.3 INTERNA
L ENERG
Y EQUATIO
N 33
1.10.4 ENTROP
Y EQUATIO
N 33
1.10.5 TOTA
L ENTHALP
Y EQUATIO
N 35
1.10.6 INTERNA
L ENTHALP
Y AN
D TEMPERATUR
E EQUATION
S 35
1.11 SPECIAL SOLUTIONS OF TH
E INTERNAL-ENERGY
, ENTHALPY
, AN
D MOMENTU
M EQUATION
S 36
XII
CONTENTS
1.11.1 ISENTROPIC SOLUTION OF TH
E INTERNAL ENERGY EQUATION 36
1.11.2 ADIABATIC- AND INVISCID-FLOW SOLUTION OF THE TOTAL-ENTHALPY
EQUATION 37
1.11.3 ISENTROPIC SOLUTION OF THE MOMENTUM EQUATION 38
2 CONSTITUTIV
E AND STAT
E EQUATION
S 4
1
2.1 NAVIER-STOKES STRESS TENSOR 41
2.2 HEAT CONDUCTION LAW 43
2.3 TRANSPORT AND THERMO-MECHANICAL PROPERTIES 43
2.4 SECOND-LAW CONSTRAINTS ON TRANSPORT COEFFICIENTS 45
2.5 EQUATIONS OF STAT
E 46
2.6 SPEED OF SOUND 47
2.7 ISENTROPIC CONSTRAINT ON DERIVATIVES OF DENSITY AND ENERGY 48
3 STAT
E EQUATION
S FOR REACTIN
G AI
R 51
3.1 THERMO-CHEMICAL EQUATIONS 52
3.1.1 SPECIES MASSES AND MOLES 52
3.1.2 MASS AND MOLE FRACTIONS 53
3.1.3 PRESSURE, INTERNAL-ENERGY, MASS-FRACTION EQUATIONS 54
3.1.4 PERFECT-AIR EQUATIONS 56
3.1.5 NON-DIMENSIONAL REACTING-AIR EQUATIONS OF STAT
E 58
3.1.6 CHEMICAL AND THERMODYNAMICS PARAMETERS 61
3.1.7 CHEMICAL EQUILIBRIUM FUNCTIONS 62
3.2 ALGEBRAIC SOLUTION 63
3.3 CALCULATION OF
Y
3
AND
T
65
3.3.1 NUMERICAL SOLUTION 65
3.3.2 ITERATION PARTIAL DERIVATIVES 66
3.4 PARTIAL DERIVATIVES OF
T,
YI,
Y
2
, Y
3
, Y4,
Y"
5
WITH RESPECT TO
P
AND E 69
3.4.1 DERIVATIVES OF
T
AND
Y
3
69
3.4.2 DERIVATIVES OF YI,
Y
2
,
Y"
4
,
Y
5
70
3.5 PRESSURE AND ITS THERMODYNAMIC DERIVATIVES 72
3.6 JACOBIAN PARTIAL DERIVATIVES OF PRESSURE AND TEMPERATURE 72
3.7 DERIVATIVES OF
P
AND
YI
WITH RESPECT TO
P, T,
DERIVATIVES OF
P
WITH RESPECT
TO
P
AND
T,
AND DERIVATIVES OF
T
WITH RESPECT TO
P
AND
P
73
3.8 THERMODYNAMIC PROPERTIES WITH
P
AND
T
AS INDEPENDENT VARIABLES 74
3.9 SPECIFIC HEATS 75
3.9.1 SPECIFIC HEAT
C
V
76
3.9.2 SPECIFIC HEAT
C
P
76
3.10 SPEED OF SOUND 78
3.11 COMPUTATIONAL RESULTS 79
3.12 PERFORMANCE SUMMARY 91
4 EULER AND NAVIE
R STOKE
S SYSTEM
S 9
3
4.1 COMPRESSIBLE FLOWS ' 95
4.1.1 CONSERVATION FORM 95
4.1.2 NON-DIMENSIONAL SYSTEM 96
CONTENTS
XIII
4.1.3 VARIATIONAL FORMULATION 98
4.2 LOW SPEED AND INCOMPRESSIBLE FLOWS 98
4.2.1 CONTINUITY EQUATION 99
4.2.2 MOMENTUM EQUATION 99
4.2.3 TEMPERATURE EQUATION 100
4.2.4 GOVERNING SYSTEM 103
4.2.5 NON-DIMENSIONAL SYSTEM 103
4.2.6 VARIATIONAL FORMULATION 105
QUASI ONE-DIMENSIONAL AND FREE-SURFACE EQUATIONS 107
5.1 AREA AVERAGES 107
5.2 QUASI ONE-DIMENSIONAL EULER EQUATIONS 108
5.2.1 CONTINUITY EQUATION 108
5.2.2 GENERALIZED LINEAR-MOMENTUM EQUATION 110
5.2.3 ENERGY EQUATION 114
5.2.4 COMPRESSIBLE-FLOW SYSTEM 118
5.2.5 INCOMPRESSIBLE-FLOW SYSTEM 120
5.3 OPEN-CHANNEL CONFIGURATION 121
5.3.1 DEPTH AVERAGES 122
5.3.2 AREA AVERAGES 123
5.4 QUASI ONE-DIMENSIONAL FREE-SURFACE OPEN-CHANNEL FLOW EQUATIONS 125
5.4.1 CONTINUITY EQUATION 126
5.4.2 MOMENTUM EQUATION 128
5.4.3 ENERGY EQUATION 132
5.4.4 QUASI ONE-DIMENSIONAL FREE-SURFACE SYSTEM 135
5.5 TWO-DIMENSIONAL FREE-SURFACE EQUATIONS 137
5.5.1 CONTINUITY EQUATION 137
5.5.2 MOMENTUM EQUATION 137
5.5.3 ENERGY EQUATION 142
5.5.4 NON-DIMENSIONAL 2-D FREE-SURFACE EQUATIONS 146
OVERVIEW OF CF
D ALGORITHM DEVELOPMENT 149
6.1 MATHEMATICAL MODEL 150
6.2 SPATIAL APPROXIMATION: DISCRETIZATION 154
6.2.1 STEADY-SOLUTION MONOTONICITY 155
6.2.2 UNSTEADY-SOLUTION STABILITY 157
6.3 TIME INTEGRATION 160
6.4 SOLUTION OF NON-LINEAR SYSTEMS 164
THE FINIT
E ELEMENT METHO
D 167
7.1 VARIATIONAL WEIGHTED INTEGRAL STATEMENTS 169
7.1.1 LEAST SQUARES STATEMENTS 169
7.1.2 REPRESENTATIVE OPTIMAL SOLUTIONS 171
7.1.3 FLUID DYNAMICS EQUATIONS FROM A VARIATIONAL PRINCIPLE 173
7.2 INTEGRALS FROM GAUSS' DIVERGENCE THEOREM 175
XIV
CONTENTS
7.3 WEAK DERIVATIVES AN
D INTEGRA
L STATEMEN
T 177
7.4 CHARACTERISTICS-BIA
S FORMULATIO
N 178
7.4.1 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 179
7.4.2 NON-DISCRETE STREAMLIN
E UPWIND PETROV-GALERKI
N (SUPG
) FORM .
. 180
7.5 HILBERT SPACES AN
D APPROXIMATIO
N RESULT
S 181
7.5.1 HILBER
T SPACES 181
7.5.2 APPROXIMATIO
N RESULT
S 182
7.6 CURVILINEAR COORDINAT
E TRANSFORMATION
S 182
7.6.1 AREA
S AN
D VOLUMES 182
7.6.2 TWO-DIMENSIONAL COORDINAT
E TRANSFORMATIO
N 184
7.6.3 THREE-DIMENSIONA
L COORDINAT
E TRANSFORMATIO
N 187
7.6.4 DIFFERENTIAL ARC
, AREA
, VOLUME 191
7.7 DISCRETIZED STATEMEN
T 194
7.7.1 DIFFERENTIAL AN
D INTEGRA
L CURVILINEAR-COORDINAT
E STATEMENT
S 194
7.7.2 FINIT
E ELEMENT GALERKIN FORMULATIO
N 196
7.7.3 DISCRETIZATIO
N OF SPACE 199
7.7.4 DISCRETIZATIO
N OF FUNCTION
S 200
7.7.5 A-POSTERIOR
I ACCURACY ASSESSMENT 203
7.8 BASIS FUNCTIONS
, ELEMEN
T AN
D COORDINAT
E TRANSFORMATION
S 205
7.8.1 ONE-DIMENSIONAL ELEMENT
S AN
D COORDINAT
E TRANSFORMATION
S 205
7.8.2 MULTI-DIMENSIONAL ELEMENT
S 208
7.9 ELEMENT INTEGRALS
, GAUSSIA
N QUADRATURES
, OPTIMA
L METRI
C DAT
A 211
7.9.1 ONE-DIMENSIONAL INTEGRAL
S 211
7.9.2 GAUSSIA
N QUADRATURE
S 212
7.9.3 MULTI-DIMENSIONAL INTEGRAL
S AN
D OPTIMA
L METRI
C DAT
A 213
7.10 IMPLEMENTATIO
N SEQUENCE 217
8 NON-LINEARL
Y STABL
E IMPLICI
T RUNGE-KUTT
A TIM
E INTEGRATION
S 22
5
8.1 RUNGE-KUTT
A ALGORITH
M 226
8.2 NON-LINEAR STABILIT
Y 227
8.3 LINEAR STABILIT
Y 230
8.4 IRK2
: A TWO-STAG
E DIAGONALLY IMPLICIT ALGORITH
M 231
8.4.1 NUMERICAL LINEAR ALGEBR
A 231
8.4.2 STABILIT
Y CONSTRAINT
S 232
8.4.3 ACCURACY AN
D B - CONSISTENC
Y / CONVERGENCE CONSTRAINT
S 233
8.4.4 SOLUTION OF TH
E IR
K COEFFICIENT EQUATION
S 234
8.4.5 ACCURACY AN
D STABILIT
Y PERFORMANCE 235
8.5 ONE- AN
D TWO-STAGE DIAGONALLY IMPLICIT ALGORITHM
S 237
8.6 TIM
E STE
P SIZE ADJUSTMEN
T 237
8.7 THEORETICA
L COMPARISON
S 239
9 ONE-DIMENSIONA
L NON-DISCRET
E CHARACTERISTICS-BIA
S RESOLUTIO
N 24
1
9.1 SOLUTIONS OF NON-LINEAR HYPERBOLI
C EQUATION
S 242
9.1.1 SOLUTIONS AN
D CHARACTERISTI
C LINES 243
9.1.2 BREAKIN
G TIM
E 246
CONTENTS
XV
9.1.3 SHOCKS 247
9.1.4 HYPERBOLIC SYSTEMS 249
9.2 PARABOLIC PERTURBATION EQUATIONS 250
9.2.1 SCALAR EQUATIONS 250
9.2.2 PERTURBATION SYSTEMS 252
9.3 CHARACTERISTICS-BIAS RESOLUTION 254
9.3.1 UPSTREAM-BIAS TIME DERIVATIVE AND SOURCE 254
9.3.2 FLUX JACOBIAN DECOMPOSITION AND UPSTREAM-BIAS INTEGRAL AVERAGE .
255
9.3.3 CHARACTERISTICS-BIAS FLUX 255
9.3.4 FLUX VECTOR SPLITTING 256
9.3.5 FLUX DIFFERENCE SPLITTING 257
9.3.6 CHARACTERISTICS-BIAS SYSTEM 258
9.4 GALILEAN INVARIANCE AND CHARACTERISTICS-BIAS DIFFUSION 259
9.5 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 262
9.6 NON-DISCRETE STREAMLINE UPWIND PETROV-GALERKIN (SUPG) FORM 263
10 CHARACTERISTICS-BIA
S CONTROLLE
R AN
D LENGT
H 265
10.1
MEASURE OF SOLUTION SMOOTHNESS 265
10.1.1 ONE-DIMENSIONAL FLOWS 267
10.1.2 MULTI-DIMENSIONAL FLOWS 268
10.2 CORRELATION BETWEEN
P
AND -0 270
10.3 MULTI-DIMENSIONAL LENGTH
E
273
10.4 MAGNITUDE OF
(P, IFF,
EIP
276
11 COMPUTATIONA
L ANALYSI
S OF QUASI-1-
D INCOMPRESSIBL
E FLOW
S 279
11.1 SLIGHT-COMPRESSIBILITY CONTINUITY EQUATION 280
11.2 INCOMPRESSIBLE FLOW "CHARACTERISTICS" 281
11.3 SLIGHT-COMPRESSIBILITY ACOUSTICS EQUATIONS 283
11.4 INCOMPRESSIBLE-FLOW ACOUSTICS-CONVECTION SYSTEM-MATRIX
DECOMPOSITION . . 284
11.4.1 CONVECTION AND PRESSURE-JACOBIAN COMPONENTS 285
11.4.2 ACOUSTIC COMPONENTS 285
11.4.3 COMBINATION OF MATRIX DECOMPOSITIONS 286
11.5 CHARACTERISTICS-BIAS SYSTEM MATRIX 287
11.5.1 CONSISTENT UPSTREAM-BIAS 288
11.5.2 UPSTREAM-BIAS EIGENVALUES AND FUNCTIONS
A
AND
S
288
11.6 INCOMPRESSIBLE-FLOW FORMULATION 290
11.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 292
11.8 FINITE ELEMENT WEAK STATEMENT 294
11.8.1 GALERKIN FINITE ELEMENT EXPANSIONS AND INTEGRALS 295
11.8.2 DISCRETE UPSTREAM BIAS 297
11.8.3 BOUNDARY EQUATIONS AND PRESSURE BOUNDARY CONDITION 298
11.9 IMPLICIT RUNGE KUTT
A TIME INTEGRATION 299
LL.LOREFERENCE EXACT SOLUTIONS 302
11.10.1 GENERAL SOLUTION 302
11.10.2 PARTICULAR SOLUTION 303
XVI
CONTENTS
11.10.3 SOLUTION PROPERTIE
S 303
11.10.4 TRANSIEN
T SOLUTION 304
11.10.5 STEAD
Y STAT
E SOLUTION 305
11.10.6 SIMILARITY SOLUTION 307
11.11 COMPUTATIONA
L RESULT
S 308
11.11.1 UNSTEAD
Y FLOW: PERIODI
C OUTLE
T PRESSUR
E 310
11.11.2 TRANSIEN
T AN
D STEAD
Y STAT
E FLOW 314
11.12 COMPUTATIONA
L PERFORMANCE 319
1
2 NUMERICA
L STUD
Y O
F GENERALIZE
D QUASI-1-
D FRE
E SURFAC
E FLOW
S 32
1
12.1 ONE-DIMENSIONAL FREE-SURFACE FLOW CHARACTERISTIC
S 322
12.2 GRAVITY-WAVE EQUATION
S 325
12.3 FREE-SURFACE GRAVITY-WAVE-CONVECTION FLU
X JACOBIA
N DECOMPOSITION .
. 327
12.3.1 CONVECTION AN
D PRESSURE-GRADIEN
T COMPONENT
S 327
12.3.2 GRAVITY-WAVE COMPONENT
S 328
12.3.3 COMBINATIO
N OF FLUX-JACOBIA
N DECOMPOSITIONS 330
12.4 CHARACTERISTICS-BIA
S FLU
X DIVERGENCE 331
12.4.1 CONSISTEN
T UPSTREAM-BIA
S 331
12.4.2 UPSTREAM-BIA
S EIGENVALUES AN
D FUNCTION
S
A
AN
D
D
332
12.5 VARIATIONA
L STATEMEN
T AN
D BOUNDAR
Y CONDITION
S 335
12.6 FINIT
E ELEMENT WEAK STATEMEN
T 338
12.6.1 GALERKIN FINIT
E ELEMEN
T EXPANSION
S AN
D INTEGRAL
S 339
12.6.2 DISCRETE UPSTREA
M BIA
S 340
12.6.3 BOUNDAR
Y EQUATION
S AN
D PRESSUR
E BOUNDAR
Y CONDITION
S 342
12.7 IMPLICIT RUNG
E KUTT
A TIM
E INTEGRATIO
N 343
12.8 REFERENCE EXAC
T SOLUTIONS 345
12.8.1 CHANNEL-WIDT
H RULE 345
12.8.2 EXAC
T INTEGRAL
S 346
12.8.3 SIMILARITY SOLUTION 347
12.8.4 HYDRAULI
C JUM
P CALCULATIO
N 348
12.9 COMPUTATIONA
L RESULT
S 351
12.9.1 WORK DRIVEN FLOWS 352
12.9.2 MASS-TRANSFER FLOWS 354
12.9.3 ADIABATI
C SMOOT
H AN
D SHOCKED FLOWS WIT
H FRICTIO
N 357
12.9.4 SHOCKED FLOWS WIT
H FRICTION, MASS TRANSFER AN
D BED SLOPE 361
12.9.5 SMOOT
H AN
D SHOCKED FLOWS OVER A BUM
P 364
12.9.6 DAM-BREA
K FLOW 370
12.9.7 FLOW WIT
H HYDRAULI
C JUMP
S IN A VARIABLE-WIDT
H CHANNE
L 376
12.9.8 FLOW WIT
H HYDRAULI
C JUMP
S IN A VARIABLE-WIDT
H CHANNE
L
WIT
H FRICTION, SLOPING BED, MASS AS WELL AS HEA
T TRANSFER 382
12.9.9 CONVERGENCE T
O STEAD
Y STAT
E 385
12.10COMPUTATIONA
L PERFORMANCE 386
CONTENTS
XVII
13 CF
D INVESTIGATIO
N OF GENERALIZE
D QUASI-1-
D COMPRESSIBL
E FLOW
S 389
13.1 CHARACTERISTICS ANALYSIS 390
13.2 ACOUSTICS EQUATIONS 393
13.3 ACOUSTICS-CONVECTION FLUX JACOBIAN DECOMPOSITION 395
13.3.1 CONVECTION AND PRESSURE-GRADIENT COMPONENTS 395
13.3.2 ACOUSTIC COMPONENTS 396
13.3.3 COMBINATION OF FLUX-JACOBIAN DECOMPOSITIONS 398
13.4 CHARACTERISTICS-BIAS FLUX-DIVERGENCE 399
13.4.1 CONSISTENT UPSTREAM-BIAS 399
13.4.2 UPSTREAM-BIAS EIGENVALUES AND FUNCTIONS
A
AND
S
400
13.5 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 403
13.6 FINITE ELEMENT WEAK STATEMENT 406
13.6.1 GALERKIN FINITE ELEMENT EXPANSIONS AND INTEGRALS 407
13.6.2 DISCRETE UPSTREAM BIAS 408
13.6.3 BOUNDARY EQUATIONS AND PRESSURE BOUNDARY CONDITION 410
13.7 IMPLICIT RUNGE KUTT
A TIME INTEGRATION 411
13.8 REFERENCE EXACT SOLUTIONS 413
13.8.1 SMOOTH-FLOW PRESSURE INTEGRAL 414
13.8.2 STEADY-STATE EQUATIONS 415
13.8.3 AREA RULE 415
13.8.4 EXACT INTEGRALS 416
13.8.5 SIMILARITY SOLUTION 417
13.8.6 CALCULATION OF SHOCKED FLOWS 420
13.9 COMPUTATIONAL RESULTS 423
13.9.1 SOD'S SHOCK TUBE FLOW 424
13.9.2 HEAT-TRANSFER FLOWS 427
13.9.3 MASS-TRANSFER FLOWS 429
13.9.4 MASS- AND HEAT-TRANSFER FLOWS 431
13.9.5 WORK DRIVEN FLOWS 433
13.9.6 ADIABATIC SMOOTH AND SHOCKED FLOWS WITH WALL FRICTION 435
13.9.7 SHOCKED FLOWS WITH WALL FRICTION, HEAT, MASS, AND WORK TRANSFER .
. 439
13.9.8 SHAPIRO'S BENCHMARK 441
13.9.9 FLOWS IN A DIVERGING NOZZLE 443
13.9.10 ADIABATIC SMOOTH AND SHOCKED FLOWS IN A CONVERGING-DIVERGING
NOZZLE448
13.9.11 SHOCKED NOZZLE FLOWS WITH WALL FRICTION,
HEATING, MASS AND WORK TRANSFER 454
13.9.12 CONVERGENCE TO STEADY STATE 458
13.10COMPUTATIONAL PERFORMANCE 459
14 MULTI-DIMENSIONA
L CHARACTERISTIC
S AN
D CHARACTERISTICS-BIA
S SYSTEM
S 46
1
14.1 HYPERBOLIC EQUATIONS AND ELLIPTIC, PARABOLIC, HYPERBOLIC SYSTEMS
462
14.1.1 SCALAR EQUATIONS 462
14.1.2 NON-LINEAR WAVE-LIKE VECTOR SOLUTIONS 464
14.1.3 NON-LINEAR ELLIPTIC, PARABOLIC, HYPERBOLIC SYSTEMS 467
14.2 WAVE-PROPAGATION AND CHARACTERISTIC SURFACES 468
XVIII
CONTENTS
14.2.1 CHARACTERISTIC SURFACES 468
14.2.2 CHARACTERISTIC AND DISCONTINUITY SURFACES 469
14.3 CHARACTERISTIC CONES AND HYPERBOLIC WAVE PROPAGATION 470
14.3.1 GALILEAN TRANSFORMATION 470
14.3.2 CHARACTERISTIC CONES AND WAVE PROPAGATION PATTERN
S 472
14.4 PARABOLIC PERTURBATION SYSTEM 477
14.5 CHARACTERISTICS-BIAS REPRESENTATION 480
14.5.1 UPSTREAM-BIAS TIME DERIVATIVE, SOURCE, VISCOUS-FLUX DIVERGENCE .
. 481
14.5.2 FLUX JACOBIAN DECOMPOSITION AND UPSTREAM-BIAS INTEGRAL AVERAGE .
482
14.5.3 CHARACTERISTICS-BIAS FLUX 483
14.5.4 UPSTREAM-BIAS STABILITY CONDITION 483
14.5.5 INCORPORATION OF FLUX-VECTOR AND FLUX-DIFFERENCE SPLITTINGS 485
14.5.6 CHARACTERISTICS-BIAS SYSTEM 486
14.6 GALILEAN INVARIANCE AND CHARACTERISTICS-BIAS DIFFUSION 487
14.7 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 491
14.8 NON-DISCRETE STREAMLINE UPWIND PETROV-GALERKIN (SUPG) FORM 491
15 MULTI-DIMENSIONA
L INCOMPRESSIBL
E FLOW
S 49
3
15.1 SLIGHT-COMPRESSIBILITY SYSTEM 494
15.1.1 SLIGHT-COMPRESSIBILITY CONTINUITY EQUATION 494
15.1.2 EULER AND NAVIER-STOKES EQUATIONS 495
15.2 SLIGHT-COMPRESSIBILITY ACOUSTICS EQUATIONS 496
15.2.1 MATRIX FORM 496
15.2.2 STREAMLINE AND CROSSFLOW COMPONENTS 498
15.2.3 SIMILARITY TRANSFORMATION 501
15.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 503
15.3.1 POLAR VARIATION OF CHARACTERISTIC SPEEDS 504
15.3.2 WAVE PROPAGATION REGION AND CHARACTERISTIC CONE 506
15.3.3 PHYSICAL MULTI-DIMENSIONAL UPSTREAM BIAS 510
15.4 ACOUSTICS-CONVECTION CHARACTERISTICS-BIAS DECOMPOSITION 511
15.4.1 2-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 511
15.4.2 2-D ACOUSTIC COMPONENTS 512
15.4.3 COMBINATION OF 2-D ACOUSTICS-CONVECTION DECOMPOSITIONS 514
15.4.4 3-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 515
15.4.5 3-D ACOUSTIC COMPONENTS 517
15.4.6 COMBINATION OF 3-D ACOUSTICS-CONVECTION DECOMPOSITIONS 519
15.5 CHARACTERISTICS-BIAS SYSTEM MATRIX 520
15.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE-DIRECTIONAL UPSTREAM
BIAS 522
15.5.2 UPSTREAM-BIAS EIGENVALUES 523
15.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 523
15.5.4 UPSTREAM-BIAS VECTORS
A,A
NL
,A
N2
524
15.5.5 UPSTREAM-BIAS FUNCTIONS A
,
5, EX
N
526
15.6 POLAR VARIATION OF UPSTREAM-BIAS 527
15.7 INCOMPRESSIBLE-FLOW FORMULATION 529
15.8 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 532
CONTENTS
XIX
15.9 FINITE ELEMENT GALERKIN WEAK STATEMENT 536
15.10IMPLICIT RUNGE-KUTTA TIME INTEGRATION 540
15.11COMPUTATIONAL PERFORMANCE 541
15.11.1 BACKWARD-FACING STEP DIFFUSER FLOW 542
15.11.2 NATURAL CONVECTION 549
15.11.3 LID-DRIVEN CAVITY FLOW 556
15.11.4LID- AND BUOYANCY-DRIVEN CAVITY FLOW 563
16 MULTI-DIMENSIONA
L FREE-SURFACE FLOW
S 571
16.1 GOVERNING EQUATIONS 572
16.2 GRAVITY-WAVE EQUATIONS 572
16.2.1 STREAMLINE AND CROSSFLOW COMPONENTS 573
16.2.2 SIMILARITY TRANSFORMATION 574
16.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 575
16.3.1 POLAR VARIATION OF CHARACTERISTIC SPEEDS 576
16.3.2 REGIONS OF SUPERCRITICAL AND SUBCRITICAL WAVE PROPAGATION 578
16.3.3 FREE-SURFACE FLOW CHARACTERISTIC CONES 578
16.3.4 PHYSICAL MULTI-DIMENSIONAL UPSTREAM BIAS 582
16.4 GRAVITY-WAVE-CONVECTION FLUX DIVERGENCE DECOMPOSITION 584
16.4.1 CONVECTION AND PRESSURE-GRADIENT COMPONENTS 584
16.4.2 GRAVITY-WAVE COMPONENTS 586
16.4.3 COMBINATION OF FLUX DIVERGENCE DECOMPOSITIONS 588
16.5 CHARACTERISTICS-BIAS FLUX-DIVERGENCE 590
16.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE DIRECTIONAL UPSTREAM
BIAS 591
16.5.2 UPSTREAM-BIAS EIGENVALUES AND OBLIQUE-JUMP CAPTURING 591
16.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 592
16.5.4 UPSTREAM-BIAS FUNCTIONS A
, A
, AND
S
593
16.5.5 CROSSFLOW UPSTREAM FUNCTION
OC
N
593
16.5.6 VARIATIONS OF
A, S, CX
N
595
16.6 POLAR VARIATION OF UPSTREAM-BIAS 596
16.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 598
16.7.1 CHARACTERISTICS-BIAS EULER AND NAVIER-STOKES SYSTEMS 599
16.7.2 WEAK STATEMENT AND BOUNDARY CONDITIONS 600
16.8 FINITE ELEMENT GALERKIN WEAK STATEMENT 605
16.9 IMPLICIT RUNGE-KUTTA TIME INTEGRATION 607
16.10COMPUTATIONAL PERFORMANCE 608
16.10.1 ASYMMETRIC DAM-BREAK FLOW 609
16.10.2 BACKWARD-FACING STEP DIFFUSER FLOW 614
16.10.3 STREAM-DRIVEN INLET FLOW 620
16.10.4 FR=2.5 HYDRAULIC-JUMP REFLECTION 628
16.10.5 FR=5.0 SUPERCRITICAL FLOW 631
XX
CONTENTS
17 MULTI-DIMENSIONA
L COMPRESSIBL
E FLOW
S 63
5
17.1 EULER AND NAVIER-STOKES SYSTEMS 636
17.1.1 2-D FORMULATION 637
17.1.2 3-D FORMULATION 637
17.1.3 DEPENDENT VARIABLES 638
17.1.4 CONSTITUTIVE RELATIONS 638
17.1.5 EQUATIONS OF STATE AND SPEED OF SOUND 638
17.2 ACOUSTICS EQUATIONS AND STREAMLINE AND CROSSFLOW COMPONENTS 639
17.2.1 ACOUSTICS SYSTEMS 640
17.2.2 STREAMLINE AND CROSSFLOW COMPONENTS 643
17.2.3 SIMILARITY TRANSFORMATION 646
17.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 648
17.3.1 CHARACTERISTIC VELOCITY COMPONENTS 648
17.3.2 POLAR VARIATION OF CHARACTERISTIC SPEEDS 650
17.3.3 REGIONS OF SUPERSONIC AND SUBSONIC WAVE PROPAGATION 653
17.4 ACOUSTICS-CONVECTION EULER FLUX DIVERGENCE DECOMPOSITION 655
17.4.1 2-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 656
17.4.2 2-D ACOUSTIC COMPONENTS 657
17.4.3 COMBINATION OF 2-D ACOUSTICS-CONVECTION
CHARACTERISTICS-BIAS DECOMPOSITIONS 660
17.4.4 3-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 662
17.4.5 3-D ACOUSTIC COMPONENTS 663
17.4.6 COMBINATION OF 3-D ACOUSTICS-CONVECTION
CHARACTERISTICS-BIAS DECOMPOSITIONS 666
17.5 CHARACTERISTICS-BIAS EULER FLUX DIVERGENCE 668
17.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE-DIRECTIONAL UPSTREAM
BIAS 670
17.5.2 UPSTREAM-BIAS EIGENVALUES AND OBLIQUE-SHOCK CAPTURING 671
17.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 672
17.5.4 UPSTREAM-BIAS FUNCTIONS A
, A
, AND
6
673
17.5.5 CROSSFLOW UPSTREAM-BIAS FUNCTION
A
N
675
17.5.6 VARIATIONS OF A
,
S, A
N
677
17.6 POLAR VARIATION OF UPSTREAM-BIAS 678
17.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 681
17.7.1 CHARACTERISTICS-BIAS EULER AND NAVIER-STOKES SYSTEMS 681
17.7.2 WEAK STATEMENT AND BOUNDARY CONDITIONS 684
17.8 FINITE ELEMENT GALERKIN WEAK STATEMENT 688
17.9 IMPLICIT RUNGE-KUTTA TIME INTEGRATION 691
17.10COMPUTATIONAL RESULTS 692
17.10.1 HYPERSONIC BLUNT-BODY FLOW 692
17.10.2 AIRFOIL FLOWS 696
17.10.3 INLET FLOWS 702
17.10.4 CONVERGENCE T
O STEADY STATE 709
17.11 COMPUTATIONAL PERFORMANCE 709 |
| adam_txt |
JOE IANNELLI
CHARACTERISTIC
S FINITE
ELEMENT METHOD
S
IN COMPUTATIONA
L FLUID
DYNAMIC
S
WITH 384 FIGURES
Q SPRINGER
CONTENTS
PREFAC
E VI
I
A BRIE
F HISTOR
Y O
F THEORETICA
L AN
D COMPUTATIONA
L FLUI
D DYNAMIC
S XXII
I
1 GOVERNIN
G EQUATION
S O
F FLUI
D MECHANIC
S 1
1.1 FLUI
D PARTICL
E 1
1.2 MATHEMATICA
L DESCRIPTIO
N OF FLUI
D FLOW 4
1.3 TRANSPOR
T THEORE
M 8
1.3.1 SURFACE INTEGRA
L FOR
M 9
1.3.2 DIVERGENCE FORM 11
1.4 FLOWING AN
D STATIONAR
Y FLUI
D VOLUMES 13
1.5 STRESS TENSOR 13
1.5.1 GEOMETR
Y OF A TETRAHEDRO
N 13
1.5.2 SURFACE TRACTIO
N 15
1.5.3 STRES
S TENSOR SYMMETR
Y 16
1.5.4 NORMA
L STRESSES 17
1.5.5 STRESS INVARIANT
, MECHANICAL PRESSUR
E AN
D DEVIATORIC STRESSES 18
1.6 FLOW STAT
E VARIABLES 19
1.7 FUNDAMENTA
L EQUATION
S 20
1.7.1 CONSERVATION OF MASS: TH
E CONTINUIT
Y EQUATIO
N 20
1.7.2 SECOND LAW OF MECHANICS: TH
E LINEAR MOMENTU
M EQUATIO
N 21
1.7.3 TH
E FIRS
T LAW OF THERMODYNAMICS
: TH
E TOTA
L ENERG
Y EQUATIO
N .
. 23
1.8 CONSEQUENCES OF MASS CONSERVATIO
N 26
1.8.1 SUBSTANTIV
E DERIVATIVE 26
1.8.2 SUBSTANTIVE-DERIVATIV
E FORM OF TH
E TRANSPOR
T THEORE
M 27
1.8.3 INTERCHANG
E OF DIFFERENTIATION ORDE
R FOR MASS AN
D TIM
E 27
1.9 VELOCITY DIVERGENCE 28
1.9.1 PHYSICA
L SIGNIFICANCE 28
1.9.2 EQUATION
S FOR A FLUI
D PARTICL
E 28
1.10 ENERG
Y EQUATION
S 29
1.10.1 KINETI
C ENERG
Y EQUATIO
N 30
1.10.2 RIGID-MOTION AN
D DEFORMATION WORK 31
1.10.3 INTERNA
L ENERG
Y EQUATIO
N 33
1.10.4 ENTROP
Y EQUATIO
N 33
1.10.5 TOTA
L ENTHALP
Y EQUATIO
N 35
1.10.6 INTERNA
L ENTHALP
Y AN
D TEMPERATUR
E EQUATION
S 35
1.11 SPECIAL SOLUTIONS OF TH
E INTERNAL-ENERGY
, ENTHALPY
, AN
D MOMENTU
M EQUATION
S 36
XII
CONTENTS
1.11.1 ISENTROPIC SOLUTION OF TH
E INTERNAL ENERGY EQUATION 36
1.11.2 ADIABATIC- AND INVISCID-FLOW SOLUTION OF THE TOTAL-ENTHALPY
EQUATION 37
1.11.3 ISENTROPIC SOLUTION OF THE MOMENTUM EQUATION 38
2 CONSTITUTIV
E AND STAT
E EQUATION
S 4
1
2.1 NAVIER-STOKES STRESS TENSOR 41
2.2 HEAT CONDUCTION LAW 43
2.3 TRANSPORT AND THERMO-MECHANICAL PROPERTIES 43
2.4 SECOND-LAW CONSTRAINTS ON TRANSPORT COEFFICIENTS 45
2.5 EQUATIONS OF STAT
E 46
2.6 SPEED OF SOUND 47
2.7 ISENTROPIC CONSTRAINT ON DERIVATIVES OF DENSITY AND ENERGY 48
3 STAT
E EQUATION
S FOR REACTIN
G AI
R 51
3.1 THERMO-CHEMICAL EQUATIONS 52
3.1.1 SPECIES MASSES AND MOLES 52
3.1.2 MASS AND MOLE FRACTIONS 53
3.1.3 PRESSURE, INTERNAL-ENERGY, MASS-FRACTION EQUATIONS 54
3.1.4 PERFECT-AIR EQUATIONS 56
3.1.5 NON-DIMENSIONAL REACTING-AIR EQUATIONS OF STAT
E 58
3.1.6 CHEMICAL AND THERMODYNAMICS PARAMETERS 61
3.1.7 CHEMICAL EQUILIBRIUM FUNCTIONS 62
3.2 ALGEBRAIC SOLUTION 63
3.3 CALCULATION OF
Y
3
AND
T
65
3.3.1 NUMERICAL SOLUTION 65
3.3.2 ITERATION PARTIAL DERIVATIVES 66
3.4 PARTIAL DERIVATIVES OF
T,
YI,
Y
2
, Y
3
, Y4,
Y"
5
WITH RESPECT TO
P
AND E 69
3.4.1 DERIVATIVES OF
T
AND
Y
3
69
3.4.2 DERIVATIVES OF YI,
Y
2
,
Y"
4
,
Y
5
70
3.5 PRESSURE AND ITS THERMODYNAMIC DERIVATIVES 72
3.6 JACOBIAN PARTIAL DERIVATIVES OF PRESSURE AND TEMPERATURE 72
3.7 DERIVATIVES OF
P
AND
YI
WITH RESPECT TO
P, T,
DERIVATIVES OF
P
WITH RESPECT
TO
P
AND
T,
AND DERIVATIVES OF
T
WITH RESPECT TO
P
AND
P
73
3.8 THERMODYNAMIC PROPERTIES WITH
P
AND
T
AS INDEPENDENT VARIABLES 74
3.9 SPECIFIC HEATS 75
3.9.1 SPECIFIC HEAT
C
V
76
3.9.2 SPECIFIC HEAT
C
P
76
3.10 SPEED OF SOUND 78
3.11 COMPUTATIONAL RESULTS 79
3.12 PERFORMANCE SUMMARY 91
4 EULER AND NAVIE
R STOKE
S SYSTEM
S 9
3
4.1 COMPRESSIBLE FLOWS ' 95
4.1.1 CONSERVATION FORM 95
4.1.2 NON-DIMENSIONAL SYSTEM 96
CONTENTS
XIII
4.1.3 VARIATIONAL FORMULATION 98
4.2 LOW SPEED AND INCOMPRESSIBLE FLOWS 98
4.2.1 CONTINUITY EQUATION 99
4.2.2 MOMENTUM EQUATION 99
4.2.3 TEMPERATURE EQUATION 100
4.2.4 GOVERNING SYSTEM 103
4.2.5 NON-DIMENSIONAL SYSTEM 103
4.2.6 VARIATIONAL FORMULATION 105
QUASI ONE-DIMENSIONAL AND FREE-SURFACE EQUATIONS 107
5.1 AREA AVERAGES 107
5.2 QUASI ONE-DIMENSIONAL EULER EQUATIONS 108
5.2.1 CONTINUITY EQUATION 108
5.2.2 GENERALIZED LINEAR-MOMENTUM EQUATION 110
5.2.3 ENERGY EQUATION 114
5.2.4 COMPRESSIBLE-FLOW SYSTEM 118
5.2.5 INCOMPRESSIBLE-FLOW SYSTEM 120
5.3 OPEN-CHANNEL CONFIGURATION 121
5.3.1 DEPTH AVERAGES 122
5.3.2 AREA AVERAGES 123
5.4 QUASI ONE-DIMENSIONAL FREE-SURFACE OPEN-CHANNEL FLOW EQUATIONS 125
5.4.1 CONTINUITY EQUATION 126
5.4.2 MOMENTUM EQUATION 128
5.4.3 ENERGY EQUATION 132
5.4.4 QUASI ONE-DIMENSIONAL FREE-SURFACE SYSTEM 135
5.5 TWO-DIMENSIONAL FREE-SURFACE EQUATIONS 137
5.5.1 CONTINUITY EQUATION 137
5.5.2 MOMENTUM EQUATION 137
5.5.3 ENERGY EQUATION 142
5.5.4 NON-DIMENSIONAL 2-D FREE-SURFACE EQUATIONS 146
OVERVIEW OF CF
D ALGORITHM DEVELOPMENT 149
6.1 MATHEMATICAL MODEL 150
6.2 SPATIAL APPROXIMATION: DISCRETIZATION 154
6.2.1 STEADY-SOLUTION MONOTONICITY 155
6.2.2 UNSTEADY-SOLUTION STABILITY 157
6.3 TIME INTEGRATION 160
6.4 SOLUTION OF NON-LINEAR SYSTEMS 164
THE FINIT
E ELEMENT METHO
D 167
7.1 VARIATIONAL WEIGHTED INTEGRAL STATEMENTS 169
7.1.1 LEAST SQUARES STATEMENTS 169
7.1.2 REPRESENTATIVE OPTIMAL SOLUTIONS 171
7.1.3 FLUID DYNAMICS EQUATIONS FROM A VARIATIONAL PRINCIPLE 173
7.2 INTEGRALS FROM GAUSS' DIVERGENCE THEOREM 175
XIV
CONTENTS
7.3 WEAK DERIVATIVES AN
D INTEGRA
L STATEMEN
T 177
7.4 CHARACTERISTICS-BIA
S FORMULATIO
N 178
7.4.1 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 179
7.4.2 NON-DISCRETE STREAMLIN
E UPWIND PETROV-GALERKI
N (SUPG
) FORM .
. 180
7.5 HILBERT SPACES AN
D APPROXIMATIO
N RESULT
S 181
7.5.1 HILBER
T SPACES 181
7.5.2 APPROXIMATIO
N RESULT
S 182
7.6 CURVILINEAR COORDINAT
E TRANSFORMATION
S 182
7.6.1 AREA
S AN
D VOLUMES 182
7.6.2 TWO-DIMENSIONAL COORDINAT
E TRANSFORMATIO
N 184
7.6.3 THREE-DIMENSIONA
L COORDINAT
E TRANSFORMATIO
N 187
7.6.4 DIFFERENTIAL ARC
, AREA
, VOLUME 191
7.7 DISCRETIZED STATEMEN
T 194
7.7.1 DIFFERENTIAL AN
D INTEGRA
L CURVILINEAR-COORDINAT
E STATEMENT
S 194
7.7.2 FINIT
E ELEMENT GALERKIN FORMULATIO
N 196
7.7.3 DISCRETIZATIO
N OF SPACE 199
7.7.4 DISCRETIZATIO
N OF FUNCTION
S 200
7.7.5 A-POSTERIOR
I ACCURACY ASSESSMENT 203
7.8 BASIS FUNCTIONS
, ELEMEN
T AN
D COORDINAT
E TRANSFORMATION
S 205
7.8.1 ONE-DIMENSIONAL ELEMENT
S AN
D COORDINAT
E TRANSFORMATION
S 205
7.8.2 MULTI-DIMENSIONAL ELEMENT
S 208
7.9 ELEMENT INTEGRALS
, GAUSSIA
N QUADRATURES
, OPTIMA
L METRI
C DAT
A 211
7.9.1 ONE-DIMENSIONAL INTEGRAL
S 211
7.9.2 GAUSSIA
N QUADRATURE
S 212
7.9.3 MULTI-DIMENSIONAL INTEGRAL
S AN
D OPTIMA
L METRI
C DAT
A 213
7.10 IMPLEMENTATIO
N SEQUENCE 217
8 NON-LINEARL
Y STABL
E IMPLICI
T RUNGE-KUTT
A TIM
E INTEGRATION
S 22
5
8.1 RUNGE-KUTT
A ALGORITH
M 226
8.2 NON-LINEAR STABILIT
Y 227
8.3 LINEAR STABILIT
Y 230
8.4 IRK2
: A TWO-STAG
E DIAGONALLY IMPLICIT ALGORITH
M 231
8.4.1 NUMERICAL LINEAR ALGEBR
A 231
8.4.2 STABILIT
Y CONSTRAINT
S 232
8.4.3 ACCURACY AN
D B - CONSISTENC
Y / CONVERGENCE CONSTRAINT
S 233
8.4.4 SOLUTION OF TH
E IR
K COEFFICIENT EQUATION
S 234
8.4.5 ACCURACY AN
D STABILIT
Y PERFORMANCE 235
8.5 ONE- AN
D TWO-STAGE DIAGONALLY IMPLICIT ALGORITHM
S 237
8.6 TIM
E STE
P SIZE ADJUSTMEN
T 237
8.7 THEORETICA
L COMPARISON
S 239
9 ONE-DIMENSIONA
L NON-DISCRET
E CHARACTERISTICS-BIA
S RESOLUTIO
N 24
1
9.1 SOLUTIONS OF NON-LINEAR HYPERBOLI
C EQUATION
S 242
9.1.1 SOLUTIONS AN
D CHARACTERISTI
C LINES 243
9.1.2 BREAKIN
G TIM
E 246
CONTENTS
XV
9.1.3 SHOCKS 247
9.1.4 HYPERBOLIC SYSTEMS 249
9.2 PARABOLIC PERTURBATION EQUATIONS 250
9.2.1 SCALAR EQUATIONS 250
9.2.2 PERTURBATION SYSTEMS 252
9.3 CHARACTERISTICS-BIAS RESOLUTION 254
9.3.1 UPSTREAM-BIAS TIME DERIVATIVE AND SOURCE 254
9.3.2 FLUX JACOBIAN DECOMPOSITION AND UPSTREAM-BIAS INTEGRAL AVERAGE .
255
9.3.3 CHARACTERISTICS-BIAS FLUX 255
9.3.4 FLUX VECTOR SPLITTING 256
9.3.5 FLUX DIFFERENCE SPLITTING 257
9.3.6 CHARACTERISTICS-BIAS SYSTEM 258
9.4 GALILEAN INVARIANCE AND CHARACTERISTICS-BIAS DIFFUSION 259
9.5 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 262
9.6 NON-DISCRETE STREAMLINE UPWIND PETROV-GALERKIN (SUPG) FORM 263
10 CHARACTERISTICS-BIA
S CONTROLLE
R AN
D LENGT
H 265
10.1
MEASURE OF SOLUTION SMOOTHNESS 265
10.1.1 ONE-DIMENSIONAL FLOWS 267
10.1.2 MULTI-DIMENSIONAL FLOWS 268
10.2 CORRELATION BETWEEN
P
AND -0 270
10.3 MULTI-DIMENSIONAL LENGTH
E
273
10.4 MAGNITUDE OF
(P, IFF,
EIP
276
11 COMPUTATIONA
L ANALYSI
S OF QUASI-1-
D INCOMPRESSIBL
E FLOW
S 279
11.1 SLIGHT-COMPRESSIBILITY CONTINUITY EQUATION 280
11.2 INCOMPRESSIBLE FLOW "CHARACTERISTICS" 281
11.3 SLIGHT-COMPRESSIBILITY ACOUSTICS EQUATIONS 283
11.4 INCOMPRESSIBLE-FLOW ACOUSTICS-CONVECTION SYSTEM-MATRIX
DECOMPOSITION . . 284
11.4.1 CONVECTION AND PRESSURE-JACOBIAN COMPONENTS 285
11.4.2 ACOUSTIC COMPONENTS 285
11.4.3 COMBINATION OF MATRIX DECOMPOSITIONS 286
11.5 CHARACTERISTICS-BIAS SYSTEM MATRIX 287
11.5.1 CONSISTENT UPSTREAM-BIAS 288
11.5.2 UPSTREAM-BIAS EIGENVALUES AND FUNCTIONS
A
AND
S
288
11.6 INCOMPRESSIBLE-FLOW FORMULATION 290
11.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 292
11.8 FINITE ELEMENT WEAK STATEMENT 294
11.8.1 GALERKIN FINITE ELEMENT EXPANSIONS AND INTEGRALS 295
11.8.2 DISCRETE UPSTREAM BIAS 297
11.8.3 BOUNDARY EQUATIONS AND PRESSURE BOUNDARY CONDITION 298
11.9 IMPLICIT RUNGE KUTT
A TIME INTEGRATION 299
LL.LOREFERENCE EXACT SOLUTIONS 302
11.10.1 GENERAL SOLUTION 302
11.10.2 PARTICULAR SOLUTION 303
XVI
CONTENTS
11.10.3 SOLUTION PROPERTIE
S 303
11.10.4 TRANSIEN
T SOLUTION 304
11.10.5 STEAD
Y STAT
E SOLUTION 305
11.10.6 SIMILARITY SOLUTION 307
11.11 COMPUTATIONA
L RESULT
S 308
11.11.1 UNSTEAD
Y FLOW: PERIODI
C OUTLE
T PRESSUR
E 310
11.11.2 TRANSIEN
T AN
D STEAD
Y STAT
E FLOW 314
11.12 COMPUTATIONA
L PERFORMANCE 319
1
2 NUMERICA
L STUD
Y O
F GENERALIZE
D QUASI-1-
D FRE
E SURFAC
E FLOW
S 32
1
12.1 ONE-DIMENSIONAL FREE-SURFACE FLOW CHARACTERISTIC
S 322
12.2 GRAVITY-WAVE EQUATION
S 325
12.3 FREE-SURFACE GRAVITY-WAVE-CONVECTION FLU
X JACOBIA
N DECOMPOSITION .
. 327
12.3.1 CONVECTION AN
D PRESSURE-GRADIEN
T COMPONENT
S 327
12.3.2 GRAVITY-WAVE COMPONENT
S 328
12.3.3 COMBINATIO
N OF FLUX-JACOBIA
N DECOMPOSITIONS 330
12.4 CHARACTERISTICS-BIA
S FLU
X DIVERGENCE 331
12.4.1 CONSISTEN
T UPSTREAM-BIA
S 331
12.4.2 UPSTREAM-BIA
S EIGENVALUES AN
D FUNCTION
S
A
AN
D
D
332
12.5 VARIATIONA
L STATEMEN
T AN
D BOUNDAR
Y CONDITION
S 335
12.6 FINIT
E ELEMENT WEAK STATEMEN
T 338
12.6.1 GALERKIN FINIT
E ELEMEN
T EXPANSION
S AN
D INTEGRAL
S 339
12.6.2 DISCRETE UPSTREA
M BIA
S 340
12.6.3 BOUNDAR
Y EQUATION
S AN
D PRESSUR
E BOUNDAR
Y CONDITION
S 342
12.7 IMPLICIT RUNG
E KUTT
A TIM
E INTEGRATIO
N 343
12.8 REFERENCE EXAC
T SOLUTIONS 345
12.8.1 CHANNEL-WIDT
H RULE 345
12.8.2 EXAC
T INTEGRAL
S 346
12.8.3 SIMILARITY SOLUTION 347
12.8.4 HYDRAULI
C JUM
P CALCULATIO
N 348
12.9 COMPUTATIONA
L RESULT
S 351
12.9.1 WORK DRIVEN FLOWS 352
12.9.2 MASS-TRANSFER FLOWS 354
12.9.3 ADIABATI
C SMOOT
H AN
D SHOCKED FLOWS WIT
H FRICTIO
N 357
12.9.4 SHOCKED FLOWS WIT
H FRICTION, MASS TRANSFER AN
D BED SLOPE 361
12.9.5 SMOOT
H AN
D SHOCKED FLOWS OVER A BUM
P 364
12.9.6 DAM-BREA
K FLOW 370
12.9.7 FLOW WIT
H HYDRAULI
C JUMP
S IN A VARIABLE-WIDT
H CHANNE
L 376
12.9.8 FLOW WIT
H HYDRAULI
C JUMP
S IN A VARIABLE-WIDT
H CHANNE
L
WIT
H FRICTION, SLOPING BED, MASS AS WELL AS HEA
T TRANSFER 382
12.9.9 CONVERGENCE T
O STEAD
Y STAT
E 385
12.10COMPUTATIONA
L PERFORMANCE 386
CONTENTS
XVII
13 CF
D INVESTIGATIO
N OF GENERALIZE
D QUASI-1-
D COMPRESSIBL
E FLOW
S 389
13.1 CHARACTERISTICS ANALYSIS 390
13.2 ACOUSTICS EQUATIONS 393
13.3 ACOUSTICS-CONVECTION FLUX JACOBIAN DECOMPOSITION 395
13.3.1 CONVECTION AND PRESSURE-GRADIENT COMPONENTS 395
13.3.2 ACOUSTIC COMPONENTS 396
13.3.3 COMBINATION OF FLUX-JACOBIAN DECOMPOSITIONS 398
13.4 CHARACTERISTICS-BIAS FLUX-DIVERGENCE 399
13.4.1 CONSISTENT UPSTREAM-BIAS 399
13.4.2 UPSTREAM-BIAS EIGENVALUES AND FUNCTIONS
A
AND
S
400
13.5 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 403
13.6 FINITE ELEMENT WEAK STATEMENT 406
13.6.1 GALERKIN FINITE ELEMENT EXPANSIONS AND INTEGRALS 407
13.6.2 DISCRETE UPSTREAM BIAS 408
13.6.3 BOUNDARY EQUATIONS AND PRESSURE BOUNDARY CONDITION 410
13.7 IMPLICIT RUNGE KUTT
A TIME INTEGRATION 411
13.8 REFERENCE EXACT SOLUTIONS 413
13.8.1 SMOOTH-FLOW PRESSURE INTEGRAL 414
13.8.2 STEADY-STATE EQUATIONS 415
13.8.3 AREA RULE 415
13.8.4 EXACT INTEGRALS 416
13.8.5 SIMILARITY SOLUTION 417
13.8.6 CALCULATION OF SHOCKED FLOWS 420
13.9 COMPUTATIONAL RESULTS 423
13.9.1 SOD'S SHOCK TUBE FLOW 424
13.9.2 HEAT-TRANSFER FLOWS 427
13.9.3 MASS-TRANSFER FLOWS 429
13.9.4 MASS- AND HEAT-TRANSFER FLOWS 431
13.9.5 WORK DRIVEN FLOWS 433
13.9.6 ADIABATIC SMOOTH AND SHOCKED FLOWS WITH WALL FRICTION 435
13.9.7 SHOCKED FLOWS WITH WALL FRICTION, HEAT, MASS, AND WORK TRANSFER .
. 439
13.9.8 SHAPIRO'S BENCHMARK 441
13.9.9 FLOWS IN A DIVERGING NOZZLE 443
13.9.10 ADIABATIC SMOOTH AND SHOCKED FLOWS IN A CONVERGING-DIVERGING
NOZZLE448
13.9.11 SHOCKED NOZZLE FLOWS WITH WALL FRICTION,
HEATING, MASS AND WORK TRANSFER 454
13.9.12 CONVERGENCE TO STEADY STATE 458
13.10COMPUTATIONAL PERFORMANCE 459
14 MULTI-DIMENSIONA
L CHARACTERISTIC
S AN
D CHARACTERISTICS-BIA
S SYSTEM
S 46
1
14.1 HYPERBOLIC EQUATIONS AND ELLIPTIC, PARABOLIC, HYPERBOLIC SYSTEMS
462
14.1.1 SCALAR EQUATIONS 462
14.1.2 NON-LINEAR WAVE-LIKE VECTOR SOLUTIONS 464
14.1.3 NON-LINEAR ELLIPTIC, PARABOLIC, HYPERBOLIC SYSTEMS 467
14.2 WAVE-PROPAGATION AND CHARACTERISTIC SURFACES 468
XVIII
CONTENTS
14.2.1 CHARACTERISTIC SURFACES 468
14.2.2 CHARACTERISTIC AND DISCONTINUITY SURFACES 469
14.3 CHARACTERISTIC CONES AND HYPERBOLIC WAVE PROPAGATION 470
14.3.1 GALILEAN TRANSFORMATION 470
14.3.2 CHARACTERISTIC CONES AND WAVE PROPAGATION PATTERN
S 472
14.4 PARABOLIC PERTURBATION SYSTEM 477
14.5 CHARACTERISTICS-BIAS REPRESENTATION 480
14.5.1 UPSTREAM-BIAS TIME DERIVATIVE, SOURCE, VISCOUS-FLUX DIVERGENCE .
. 481
14.5.2 FLUX JACOBIAN DECOMPOSITION AND UPSTREAM-BIAS INTEGRAL AVERAGE .
482
14.5.3 CHARACTERISTICS-BIAS FLUX 483
14.5.4 UPSTREAM-BIAS STABILITY CONDITION 483
14.5.5 INCORPORATION OF FLUX-VECTOR AND FLUX-DIFFERENCE SPLITTINGS 485
14.5.6 CHARACTERISTICS-BIAS SYSTEM 486
14.6 GALILEAN INVARIANCE AND CHARACTERISTICS-BIAS DIFFUSION 487
14.7 NON-DISCRETE DISCONTINUOUS GALERKIN (DG) FORM 491
14.8 NON-DISCRETE STREAMLINE UPWIND PETROV-GALERKIN (SUPG) FORM 491
15 MULTI-DIMENSIONA
L INCOMPRESSIBL
E FLOW
S 49
3
15.1 SLIGHT-COMPRESSIBILITY SYSTEM 494
15.1.1 SLIGHT-COMPRESSIBILITY CONTINUITY EQUATION 494
15.1.2 EULER AND NAVIER-STOKES EQUATIONS 495
15.2 SLIGHT-COMPRESSIBILITY ACOUSTICS EQUATIONS 496
15.2.1 MATRIX FORM 496
15.2.2 STREAMLINE AND CROSSFLOW COMPONENTS 498
15.2.3 SIMILARITY TRANSFORMATION 501
15.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 503
15.3.1 POLAR VARIATION OF CHARACTERISTIC SPEEDS 504
15.3.2 WAVE PROPAGATION REGION AND CHARACTERISTIC CONE 506
15.3.3 PHYSICAL MULTI-DIMENSIONAL UPSTREAM BIAS 510
15.4 ACOUSTICS-CONVECTION CHARACTERISTICS-BIAS DECOMPOSITION 511
15.4.1 2-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 511
15.4.2 2-D ACOUSTIC COMPONENTS 512
15.4.3 COMBINATION OF 2-D ACOUSTICS-CONVECTION DECOMPOSITIONS 514
15.4.4 3-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 515
15.4.5 3-D ACOUSTIC COMPONENTS 517
15.4.6 COMBINATION OF 3-D ACOUSTICS-CONVECTION DECOMPOSITIONS 519
15.5 CHARACTERISTICS-BIAS SYSTEM MATRIX 520
15.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE-DIRECTIONAL UPSTREAM
BIAS 522
15.5.2 UPSTREAM-BIAS EIGENVALUES 523
15.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 523
15.5.4 UPSTREAM-BIAS VECTORS
A,A
NL
,A
N2
524
15.5.5 UPSTREAM-BIAS FUNCTIONS A
,
5, EX
N
526
15.6 POLAR VARIATION OF UPSTREAM-BIAS 527
15.7 INCOMPRESSIBLE-FLOW FORMULATION 529
15.8 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 532
CONTENTS
XIX
15.9 FINITE ELEMENT GALERKIN WEAK STATEMENT 536
15.10IMPLICIT RUNGE-KUTTA TIME INTEGRATION 540
15.11COMPUTATIONAL PERFORMANCE 541
15.11.1 BACKWARD-FACING STEP DIFFUSER FLOW 542
15.11.2 NATURAL CONVECTION 549
15.11.3 LID-DRIVEN CAVITY FLOW 556
15.11.4LID- AND BUOYANCY-DRIVEN CAVITY FLOW 563
16 MULTI-DIMENSIONA
L FREE-SURFACE FLOW
S 571
16.1 GOVERNING EQUATIONS 572
16.2 GRAVITY-WAVE EQUATIONS 572
16.2.1 STREAMLINE AND CROSSFLOW COMPONENTS 573
16.2.2 SIMILARITY TRANSFORMATION 574
16.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 575
16.3.1 POLAR VARIATION OF CHARACTERISTIC SPEEDS 576
16.3.2 REGIONS OF SUPERCRITICAL AND SUBCRITICAL WAVE PROPAGATION 578
16.3.3 FREE-SURFACE FLOW CHARACTERISTIC CONES 578
16.3.4 PHYSICAL MULTI-DIMENSIONAL UPSTREAM BIAS 582
16.4 GRAVITY-WAVE-CONVECTION FLUX DIVERGENCE DECOMPOSITION 584
16.4.1 CONVECTION AND PRESSURE-GRADIENT COMPONENTS 584
16.4.2 GRAVITY-WAVE COMPONENTS 586
16.4.3 COMBINATION OF FLUX DIVERGENCE DECOMPOSITIONS 588
16.5 CHARACTERISTICS-BIAS FLUX-DIVERGENCE 590
16.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE DIRECTIONAL UPSTREAM
BIAS 591
16.5.2 UPSTREAM-BIAS EIGENVALUES AND OBLIQUE-JUMP CAPTURING 591
16.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 592
16.5.4 UPSTREAM-BIAS FUNCTIONS A
, A
, AND
S
593
16.5.5 CROSSFLOW UPSTREAM FUNCTION
OC
N
593
16.5.6 VARIATIONS OF
A, S, CX
N
595
16.6 POLAR VARIATION OF UPSTREAM-BIAS 596
16.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 598
16.7.1 CHARACTERISTICS-BIAS EULER AND NAVIER-STOKES SYSTEMS 599
16.7.2 WEAK STATEMENT AND BOUNDARY CONDITIONS 600
16.8 FINITE ELEMENT GALERKIN WEAK STATEMENT 605
16.9 IMPLICIT RUNGE-KUTTA TIME INTEGRATION 607
16.10COMPUTATIONAL PERFORMANCE 608
16.10.1 ASYMMETRIC DAM-BREAK FLOW 609
16.10.2 BACKWARD-FACING STEP DIFFUSER FLOW 614
16.10.3 STREAM-DRIVEN INLET FLOW 620
16.10.4 FR=2.5 HYDRAULIC-JUMP REFLECTION 628
16.10.5 FR=5.0 SUPERCRITICAL FLOW 631
XX
CONTENTS
17 MULTI-DIMENSIONA
L COMPRESSIBL
E FLOW
S 63
5
17.1 EULER AND NAVIER-STOKES SYSTEMS 636
17.1.1 2-D FORMULATION 637
17.1.2 3-D FORMULATION 637
17.1.3 DEPENDENT VARIABLES 638
17.1.4 CONSTITUTIVE RELATIONS 638
17.1.5 EQUATIONS OF STATE AND SPEED OF SOUND 638
17.2 ACOUSTICS EQUATIONS AND STREAMLINE AND CROSSFLOW COMPONENTS 639
17.2.1 ACOUSTICS SYSTEMS 640
17.2.2 STREAMLINE AND CROSSFLOW COMPONENTS 643
17.2.3 SIMILARITY TRANSFORMATION 646
17.3 CHARACTERISTIC ANALYSIS AND VELOCITY COMPONENTS 648
17.3.1 CHARACTERISTIC VELOCITY COMPONENTS 648
17.3.2 POLAR VARIATION OF CHARACTERISTIC SPEEDS 650
17.3.3 REGIONS OF SUPERSONIC AND SUBSONIC WAVE PROPAGATION 653
17.4 ACOUSTICS-CONVECTION EULER FLUX DIVERGENCE DECOMPOSITION 655
17.4.1 2-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 656
17.4.2 2-D ACOUSTIC COMPONENTS 657
17.4.3 COMBINATION OF 2-D ACOUSTICS-CONVECTION
CHARACTERISTICS-BIAS DECOMPOSITIONS 660
17.4.4 3-D CONVECTION AND PRESSURE-GRADIENT COMPONENTS 662
17.4.5 3-D ACOUSTIC COMPONENTS 663
17.4.6 COMBINATION OF 3-D ACOUSTICS-CONVECTION
CHARACTERISTICS-BIAS DECOMPOSITIONS 666
17.5 CHARACTERISTICS-BIAS EULER FLUX DIVERGENCE 668
17.5.1 CONSISTENT MULTI-DIMENSIONAL AND INFINITE-DIRECTIONAL UPSTREAM
BIAS 670
17.5.2 UPSTREAM-BIAS EIGENVALUES AND OBLIQUE-SHOCK CAPTURING 671
17.5.3 CONDITIONS ON UPSTREAM-BIAS FUNCTIONS AND EIGENVALUES 672
17.5.4 UPSTREAM-BIAS FUNCTIONS A
, A
, AND
6
673
17.5.5 CROSSFLOW UPSTREAM-BIAS FUNCTION
A
N
675
17.5.6 VARIATIONS OF A
,
S, A
N
677
17.6 POLAR VARIATION OF UPSTREAM-BIAS 678
17.7 VARIATIONAL STATEMENT AND BOUNDARY CONDITIONS 681
17.7.1 CHARACTERISTICS-BIAS EULER AND NAVIER-STOKES SYSTEMS 681
17.7.2 WEAK STATEMENT AND BOUNDARY CONDITIONS 684
17.8 FINITE ELEMENT GALERKIN WEAK STATEMENT 688
17.9 IMPLICIT RUNGE-KUTTA TIME INTEGRATION 691
17.10COMPUTATIONAL RESULTS 692
17.10.1 HYPERSONIC BLUNT-BODY FLOW 692
17.10.2 AIRFOIL FLOWS 696
17.10.3 INLET FLOWS 702
17.10.4 CONVERGENCE T
O STEADY STATE 709
17.11 COMPUTATIONAL PERFORMANCE 709 |
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| author | Iannelli, Joe |
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| author_role | aut |
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| author_variant | j i ji |
| building | Verbundindex |
| bvnumber | BV021824476 |
| callnumber-first | T - Technology |
| callnumber-label | TA347 |
| callnumber-raw | TA347.F5 |
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| callnumber-sort | TA 3347 F5 |
| callnumber-subject | TA - General and Civil Engineering |
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| ctrlnum | (OCoLC)71200102 (DE-599)BVBBV021824476 |
| dewey-full | 532/.050151825 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.050151825 |
| dewey-search | 532/.050151825 |
| dewey-sort | 3532 850151825 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| discipline_str_mv | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| id | DE-604.BV021824476 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:55:15Z |
| indexdate | 2024-10-14T14:08:42Z |
| institution | BVB |
| isbn | 9783540251811 3540251812 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015036571 |
| oclc_num | 71200102 |
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| owner_facet | DE-703 DE-634 DE-83 DE-11 |
| physical | XXV, 727 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Computational fluid and solid mechanics |
| spelling | Iannelli, Joe Verfasser aut Characteristics finite element methods in computational fluid dynamics Joe Iannelli Berlin [u.a.] Springer 2006 XXV, 727 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational fluid and solid mechanics Literaturverz. S. 711 - 725 Finite element method Fluid dynamics Numerische Strömungssimulation (DE-588)4690080-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Numerische Strömungssimulation (DE-588)4690080-9 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 http://www.agi-imc.de/intelligentSEARCH.nsf/alldocs/30311FB3BA322894C1257020002CC14E/$File/000000016515850.PDF?OpenElement Inhaltsverzeichnis http://catdir.loc.gov/catdir/enhancements/fy0818/2006925962-d.html Beschreibung für Leser DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015036571&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iannelli, Joe Characteristics finite element methods in computational fluid dynamics Finite element method Fluid dynamics Numerische Strömungssimulation (DE-588)4690080-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4690080-9 (DE-588)4017233-8 |
| title | Characteristics finite element methods in computational fluid dynamics |
| title_auth | Characteristics finite element methods in computational fluid dynamics |
| title_exact_search | Characteristics finite element methods in computational fluid dynamics |
| title_exact_search_txtP | Characteristics finite element methods in computational fluid dynamics |
| title_full | Characteristics finite element methods in computational fluid dynamics Joe Iannelli |
| title_fullStr | Characteristics finite element methods in computational fluid dynamics Joe Iannelli |
| title_full_unstemmed | Characteristics finite element methods in computational fluid dynamics Joe Iannelli |
| title_short | Characteristics finite element methods in computational fluid dynamics |
| title_sort | characteristics finite element methods in computational fluid dynamics |
| topic | Finite element method Fluid dynamics Numerische Strömungssimulation (DE-588)4690080-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite element method Fluid dynamics Numerische Strömungssimulation Finite-Elemente-Methode |
| url | http://www.agi-imc.de/intelligentSEARCH.nsf/alldocs/30311FB3BA322894C1257020002CC14E/$File/000000016515850.PDF?OpenElement http://catdir.loc.gov/catdir/enhancements/fy0818/2006925962-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015036571&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT iannellijoe characteristicsfiniteelementmethodsincomputationalfluiddynamics |
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