Applied computational fluid dynamics techniques: an introduction based on finite element methods
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Item Description: | Nebentitel: Applied CFD techniques |
| Physical Description: | XVIII, 519 S. Ill., graph. Darst. |
| ISBN: | 047051907X 9780470519073 |
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| 100 | 1 | |a Löhner, Rainald |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied computational fluid dynamics techniques |b an introduction based on finite element methods |c Rainald Löhner |
| 246 | 1 | 3 | |a Applied CFD techniques |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2008 | |
| 300 | |a XVIII, 519 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Nebentitel: Applied CFD techniques | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Fluid dynamics |x Mathematics | |
| 650 | 4 | |a Numerical analysis | |
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| 689 | 0 | 0 | |a Numerische Strömungssimulation |0 (DE-588)4690080-9 |D s |
| 689 | 0 | 1 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | |5 DE-604 | |
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| _version_ | 1805089866115973120 |
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IMAGE 1
APPLIED
COMPUTATIONAL FLUID DYNAMICS TECHNIQUES AN INTRODUCTION BASED ON
FINITE ELEMENT METHODS
SECOND EDITION
RAINALD LOEHNER CENTER FOR COMPUTATIONAL FLUID DYNAMICS, DEPARTMENT OF
COMPUTATIONAL AND DATA SCIENCES, COLLEGE OF SCIENCES, GEORGE MASON
UNIVERSITY, FAIRFAX, VIRGINIA, USA
JOHN WILEY & SONS, LTD C
IMAGE 2
CONTENTS
FOREWORD TO THE SECOND EDITION XIV
ACKNOWLEDGEMENTS XVII
1 INTRODUCTION AND GENERAL CONSIDERATIONS 1
1.1 THE CFD CODE 4
1.2 PORTING RESEARCH CODES TO AN INDUSTRIAL CONTEXT 5
1.3 SCOPE OF THE BOOK 5
2 DATA STRUCTURES AND ALGORITHMS 7
2.1 REPRESENTATION OF A GRID 7
2.2 DERIVED DATA STRUCTURES FOR STATIC DATA 9
2.2.1 ELEMENTS SURROUNDING POINTS - LINKED LISTS 9
2.2.2 POINTS SURROUNDING POINTS 10
2.2.3 ELEMENTS SURROUNDING ELEMENTS 12
2.2.4 EDGES 14
2.2.5 EXTERNAL FACES 14
2.2.6 EDGES OF AN DEMENT 16
2.3 DERIVED DATA STRUCTURES FOR DYNAMIC DATA 17
2.3.1 N-TREES 18
2.4 SORTING AND SEARCHING 19
2.4.1 HEAP LISTS 19
2.5 PROXIMITY IN SPACE 22
2.5.1 BINS 22
2.5.2 BINARY TREES 26
2.5.3 QUADTREES AND OCTREES 28
2.6 NEAREST-NEIGHBOURS AND GRAPHS 30
2.7 DISTANCE TO SURFACE 30
3 GRID GENERATION 35
3.1 DESCRIPTION OF THE DOMAIN TO BE GRIDDED 37
3.1.1 ANALYTICAL FUNCTIONS 37
3.1.2 DISCRETEDATA 37
3.2 VARIATION OF DEMENT SIZE AND SHAPE 38
3.2.1 INTERNAL MEASURES OF GRID QUALITY 39
3.2.2 ANALYTICAL FUNCTIONS ^ 39
3.2.3 BOXES ) 39
IMAGE 3
CONTENTS
3.2.4 POINT/LINE/SURFACE SOURCES 39
3.2.5 BACKGROUND GRIDS 42
3.2.6 ELEMENT SIZE ATTACHED TO CAD DATA 43
3.2.7 ADAPTIVE BACKGROUND GRIDS 43
3.2.8 SURFACE GRIDDING WITH ADAPTIVE BACKGROUND GRIDS 45
3.3 ELEMENT TYPE 46
3.4 AUTOMATIC GRID GENERATION METHODS 47
3.5 OTHER GRID GENERATION METHODS 49
3.6 THE ADVANCING FRONT TECHNIQUE 51
3.6.1 CHECKING THE INTERSECTION OF FACES 52
3.6.2 DATA STRUCTURES TO MINIMIZE SEARCH OVERHEADS 56
3.6.3 ADDITIONAL TECHNIQUES TO INCREASE SPEED 56
3.6.4 ADDITIONAL TECHNIQUES TO ENHANCE RELIABILITY 58
3.7 DELAUNAY TRIANGULATION 59
3.7.1 CIRCUMSPHERE CALCULATIONS 61
3.7.2 DATA STRUCTURES TO MINIMIZE SEARCH OVERHEADS 62
3.7.3 BOUNDARY RECOVERY 63
3.7.4 ADDITIONAL TECHNIQUES TO INCREASE SPEED 63
3.7.5 ADDITIONAL TECHNIQUES TO ENHANCE RELIABILITY AND QUALITY 64
3.8 GRID IMPROVEMENT 65
3.8.1 REMOVAL OF BAD ELEMENTS 66
3.8.2 LAPLACIAN SMOOTHING 67
3.8.3 GRID OPTIMIZATION 67
3.8.4 SELECTIVE MESH MOVEMENT 67
3.8.5 DIAGONAL SWAPPING 68
3.9 OPTIMAL SPACE-FILLING TETRAHEDRA 70
3.10 GRIDS WITH UNIFORM CORES 72
3.11 VOLUME-TO-SURFACE MESHING 73
3.12 NAVIER-STOKES GRIDDING TECHNIQUES 75
3.12.1 DESIGN CRITERIA FOR RANS GRIDDERS 77
3.12.2 SMOOTHING OF SURFACE NORMALS 79
3.12.3 POINT DISTRIBUTION ALONG NORMALS 81
3.12.4 SUBDIVISION OF PRISMS INTO TETRAHEDRA 81
3.12.5 ELEMENT REMOVAL CRITERIA 83
3.13 FILLING SPACE WITH POINTS/ARBITRARY OBJECTS 90
3.13.1 THE ADVANCING FRONT SPACE-FILLING ALGORITHM 90
3.13.2 POINT/OBJECT PLACEMENT STENCILS 91
3.13.3 BOUNDARY CONSISTENCY CHECKS 93
3.13.4 MAXIMUM COMPACTION TECHNIQUES 93
3.13.5 ARBITRARY OBJECTS 96
3.13.6 DEPOSITION PATTERNS 96
3.14 APPLICATIONS 98
3.14.1 SPACE SHUTTLE ASCEND CONFIGURATION 99
3.14.2 PILOTEJECTINGFROMF18 100
3.14.3 CIRCLEOF WILLIS 103
3.14.4 GENERIC SUBMARINE BODY 105
IMAGE 4
V LL
3.14.5 AHMED CARBODY 105
3.14.6 TRACK 105
3.14.7 POINTCLOUDFORF117 106
3.14.8 HOPPER FUELED WITH BEANS/ELLIPSOIDS 107
3.14.9 CUBE MED WITH SPHERES OF DIFFERENT SIZES 107
4 APPROXIMATION THEORY 109
4.1 THE BASIC PROBLEM 109
4.1.1 POINT FITTING 110
4.1.2 WEIGHTED RESIDUAL METHODS 110
4.1.3 LEAST-SQUARES FORMULATION 112
4.2 CHOICE OF TRIAL FUNCTIONS 112
4.2.1 CONSTANT TRIAL FUNCTIONS IN ONE DIMENSION 112
4.2.2 LINEAR TRIAL FUNCTIONS IN ONE DIMENSION 113
4.2.3 QUADRATIC TRIAL FUNCTIONS IN ONE DIMENSION 114
4.2.4 LINEAR TRIAL FUNCTIONS IN TWO DIMENSIONS 115
4.2.5 QUADRATIC TRIAL FUNCTIONS IN TWO DIMENSIONS 117
4.3 GENERAL PROPERTIES OF SHAPE FUNCTIONS 118
4.4 WEIGHTED RESIDUAL METHODS WITH LOCAL FUNCTIONS 118
4.5 ACCURACY AND EFFORT 119
4.6 GRID ESTIMATES 121
5 APPROXIMATION OF OPERATORS 123
5.1 TAXONOMY OF METHODS 123
5.1.1 FINITE DIFFERENCE METHODS 123
5.1.2 FINITE VOLUME METHODS 124
5.1.3 GALERKIN FINITE DEMENT METHODS 124
5.1.4 PETROV-GALERKIN FINITE DEMENT METHODS 124
5.1.5 SPECTRAL DEMENT METHODS 124
5.2 THE POISSON OPERATOR 124
5.2.1 MINIMIZATION PROBLEM 125
5.2.2 AN EXAMPLE 126
5.2.3 TUTORIAL: CODE FRAGMENT FOR HEAT EQUATION 128
5.3 RECOVERY OF DERIVATIVES 130
5.3.1 FIRST DERIVATIVES 131
5.3.2 SECOND DERIVATIVES 131
5.3.3 HIGHER DERIVATIVES 132
6 DISCRETIZATION IN TIME 133
6.1 EXPLICIT SCHEMES 133
6.2 IMPLICIT SCHEMES 135
6.2.1 SITUATIONS WHERE IMPLICIT SCHEMES PAY OFF 136
6.3 A WORD OF CAUTION 136
IMAGE 5
V L LL
CONTENTS
7 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 137
7.1 DIRECT SOLVERS 137
7.1.1 GAUSSIAN ELIMINATION 137
7.1.2 CROUT ELIMINATION 139
7.1.3 CHOLESKY ELIMINATION 140
7.2 ITERATIVE SOLVERS 140
7.2.1 MATRIX PRECONDITIONING 141
7.2.2 GLOBALIZATION PROCEDURES 147
7.3 MULTIGRID METHODS 153
7.3.1 THE MULTIGRID CONCEPT 154
7.3.2 INJECTION AND PROJECTION OPERATORS 155
7.3.3 GRIDCYCLING 157
7.3.4 ALGORITHMIC COMPLEXITY AND STORAGE REQUIREMENTS 157
7.3.5 SMOOTHING 158
7.3.6 AN EXAMPLE 159
8 SIMPLE EULER/NAVIER-STOKES SOLVERS 161
8.1 GALERKIN APPROXIMATION 162
8.1.1 EQUIVALENCY WITH FVM 164
8.2 LAX-WENDROFF(TAYLOR-GALERKIN) 164
8.2.1 EXPEDITING THE RHS EVALUATION 165
8.2.2 LINEAR ELEMENTS (TRIANGLES, TETRAHEDRA) 166
8.3 SOLVING FOR THE CONSISTENT MASS MATRIX 167
8.4 ARTIFICIAL VISCOSITIES 167
8.5 BOUNDARY CONDITIONS 169
8.6 VISCOUS FLUXES 172
9 FLUX-CORRECTED TRANSPORT SCHEMES 175
9.1 ALGORITHMIC IMPLEMENTATION 176
9.1.1 THE LIMITING PROCEDURE 176
9.2 STEEPENING 178
9.3 FCT FOR TAYLOR-GALERKIN SCHEMES 179
9.4 ITERATIVE LIMITING 179
9.5 LIMITING FOR SYSTEMS OF EQUATIONS 180
9.5.1 LIMITING ANY SET OF QUANTITIES 180
9.6 EXAMPLES 181
9.6.1 SHOCKTUBE 181
9.6.2 SHOCK DIFFRACTION OVER A WALL 182
9.7 SUMMARY 183
10 EDGE-BASED COMPRESSIBLE FLOW SOLVERS 187
10.1 THE LAPLACIAN OPERATOR 188
10.2 FIRST DERIVATIVES: FIRST FORM 190
10.3 FIRST DERIVATIVES: SECOND FORM 191
10.4 EDGE-BASED SCHEMES FOR ADVECTION-DOMINATED PDES 193
10.4.1 EXACT RIEMANN SOLVER (GODUNOV SCHEME) 194
10.4.2 APPROXIMATE RIEMANN SOLVERS 195
IMAGE 6
IX
10.4.3 SCALAR LIMITED DISSIPATION 197
10.4.4 SCALAR DISSIPATION WITH PRESSURE SENSORS 197
10.4.5 SCALAR DISSIPATION WITHOUT GRADIENTS 198
10.4.6 TAYLOR-GALERKIN SCHEMES 199
10.4.7 FLUX-CORRECTED TRANSPORT SCHEMES 199
11 INCOMPRESSIBLE FLOW SOLVERS 201
11.1 THE ADVECTION OPERATOR 201
11.1.1 INTEGRATION ALONG CHARACTERISTICS 202
11.1.2 TAYLOR-GALERKIN 202
11.1.3 EDGE-BASED UPWINDING 203
11.2 THE DIVERGENCE OPERATOR 203
11.3 ARTIFICIAL COMPRESSIBILITY 206
11.4 TEMPORAL DISCRETIZATION: PROJECTION SCHEMES 206
11.5 TEMPORAL DISCRETIZATION: IMPLICIT SCHEMES 208
11.6 TEMPORAL DISCRETIZATION OF HIGHER ORDER 209
11.7 ACCELERATION TO THE STEADY STATE 210
11.7.1 LOCAL TIMESTEPPING 210
11.7.2 REDUCED PRESSURE ITERATIONS 210
11.7.3 SUBSTEPPING FOR THE ADVECTION TERMS 211
11.7.4 IMPLICIT TREATMENT OF THE ADVECTION TERMS 211
11.8 PROJECTIVE PREDICTIONOF PRESSURE INCREMENTS 212
11.9 EXAMPLES 213
11.9.1 VON KARMAN VORTEX STREET 213
11.9.2 NACA0012WING 216
11.9.3 LPD-17TOPSIDE FLOW STUDY 218
11.9.4 DARPA SUBOFF MODEL 223
11.9.5 GENERIC SUBMARINE FOREBODY VORTEX FLOW STUDY 225
12 MESH MOVEMENT 227
12.1 THE ALE FRAME OF REFERENCE 227
12.1.1 BOUNDARY CONDITIONS 228
12.2 GEOMETRIE CONSERVATION LAW 228
12.3 MESH MOVEMENT ALGORITHMS 229
12.3.1 SMOOTHINGOFTHEVELOCITYFIELD 230
12.3.2 SMOOTHING OF THE COORDINATES 233
12.3.3 PRESCRIPTION VIA ANALYTIC FUNETIONS 235
12.4 REGION OF MOVING ELEMENTS 235
12.5 PDE-BASED DISTANCE FUNETIONS 236
12.5.1 EIKONAL EQUATION 237
12.5.2 LAPLACE EQUATION 237
12.6 PENALIZATION OF DEFORMED ELEMENTS 238
12.7 SPECIAL MOVEMENT TECHNIQUES FOR RANS GRIDS 239
12.8 ROTATING PARTS/DOMAINS 240
IMAGE 7
X CONTENTS
12.9 APPLICATIONS 241
12.9.1 MULTIPLE SPHERES 241
12.9.2 PILOTEJECTIONFROMF18 242
12.9.3 DRIFTING FLEET OF SHIPS 242
13 INTERPOLATION 245
13.1 BASIC INTERPOLATION ALGORITHM 246
13.2 FASTEST 1-TIME ALGORITHM: BRUETE FORCE 247
13.3 FASTEST IV-TIME ALGORITHM: OCTREE SEARCH 247
13.4 FASTEST KNOWN VICINITY ALGORITHM: NEIGHBOUR-TO-NEIGHBOUR 249
13.5 FASTEST GRID-TO-GRID ALGORITHM: ADVANCING-FRONT VICINITY 250
13.5.1 LAYERING OF BRUTE-FORCE SEARCHES 252
13.5.2 INSIDE-OUT INTERPOLATION 253
13.5.3 MEASURING CONCAVITY 253
13.5.4 VECTORIZATION 254
13.6 CONSERVATIVE INTERPOLATION 257
13.6.1 CONSERVATIVE AND MONOTONIC INTERPOLATION 259
13.7 SURFACE-GRID-TO-SURFACE-GRID INTERPOLATION 261
13.8 PARTICLE-GRID INTERPOLATION 265
14 ADAPTIVE MESH REFINEMENT 269
14.1 OPTIMAL-MESH CRITERIA 270
14.2 ERROR INDICATORS/ESTIMATORS 271
14.2.1 ERROR INDICATORS COMMONLY USED 272
14.2.2 PROBLEMS WITH MULTIPLE SCALES 275
14.2.3 DETERMINATION OF ELEMENT SIZE AND SHAPE 276
14.3 REFINEMENT STRATEGIES 278
14.3.1 MESH MOVEMENT OR REPOSITIONING (R-METHODS) 278
14.3.2 MESH ENRICHMENT (H/P-METHODS) 278
14.3.3 ADAPTIVE REMESHING (M-METHODS) 284
14.3.4 COMBINATIONS 286
14.4 TUTORIAL: H-REFINEMENT WITH TETRAHEDRA 286
14.4.1 ALGORITHMIC IMPLEMENTATION 287
14.5 EXAMPLES 291
14.5.1 CONVECTION BETWEEN CONCENTRIC CYLINDERS 291
14.5.2 SHOCK-OBJECT INTERACTION IN TWO DIMENSIONS 294
14.5.3 SHOCK-OBJECT INTERACTION IN THREE DIMENSIONS 296
14.5.4 SHOCK-STRUCTURE INTERACTION 297
14.5.5 OBJECT FALLING INTO SUPERSONIC FREE STREAM TWO DIMENSIONS 297
15 EFFICIENT USE OF COMPUTER HARDWARE 299
15.1 REDUCTION OF CACHE-MISSES 300
15.1.1 ARRAY ACCESS IN LOOPS 300
15.1.2 POINT RENUMBERING 301
15.1.3 REORDERING OF NODES WITHIN ELEMENTS 306
15.1.4 RENUMBERING OF EDGES ACCORDING TO POINTS 306
IMAGE 8
CONTENTS XI
15.1.5 SOME TIMINGS 308
15.1.6 AGGLOMERATION TECHNIQUES 309
15.2 VECTOR MACHINES 316
15.2.1 BASIC EDGE COLOURING ALGORITHM 317
15.2.2 BACKWARD/FORWARD STRATEGY 318
15.2.3 COMBINING VECTORIZABILITY WITH DATA LOCALITY 318
15.2.4 SWITCHING ALGORITHM 319
15.2.5 REDUCED I/A LOOPS 321
15.2.6 ALTERNATIVE RHS FORMATION 326
15.3 PARALLEL MACHINES: GENERAL CONSIDERATIONS 328
15.4 SHARED-MEMORY PARALLEL MACHINES 329
15.4.1 LOCAL AGGLOMERATION 330
15.4.2 GLOBAL AGGLOMERATION 331
15.4.3 IMPLEMENTATIONAL ISSUES 333
15.5 SIMD MACHINES 334
15.6 MIMD MACHINES 336
15.6.1 GENERAL CONSIDERATIONS 337
15.6.2 LOAD BALANCING AND DOMAIN SPLITTING 337
15.6.3 PARALLEL FLOW SOLVERS 342
15.7 THE EFFECT OFMOORE'S LAW ON PARALLEL COMPUTING 344
15.7.1 THE LIFE CYCLE OF SCIENTIFIC COMPUTING CODES 346
15.7.2 EXAMPLES 348
15.7.3 THE CONSEQUENCES OFMOORE'S LAW 349
16 SPACE-MARCHING AND DEACTIVATION 351
16.1 SPACE-MARCHING 351
16.1.1 MASKING OF POINTS AND EDGES 352
16.1.2 RENUMBERING OF POINTS AND EDGES 354
16.1.3 GROUPING TO AVOID MEMORY CONTENTION 355
16.1.4 EXTRAPOLATION OF THE SOLUTION 356
16.1.5 TREATMENT OF SUBSONIC POCKETS 357
16.1.6 MEASURING CONVERGENCE 357
16.1.7 APPLICATION TO TRANSIENT PROBLEMS 358
16.1.8 MACRO-BLOCKING 359
16.1.9 EXAMPLES FOR SPACE-MARCHING AND BLOCKING 360
16.2 DEACTIVATION 365
16.2.1 EXAMPLES OF DYNAMIC DEACTIVATION 366
17 OVERLAPPING GRIDS 371
17.1 INTERPOLATION CRITERIA 372
17.2 EXTERNAL BOUNDARIES AND DOMAINS 373
17.3 INTERPOLATION: INITIALIZATION 373
17.4 TREATMENT OF DOMAINS THAT ARE PARTIALLY OUTSIDE 375
17.5 REMOVAL OF INACTIVE REGIONS 375
17.6 INCREMENTAL INTERPOLATION 377
17.7 CHANGES TO THE FLOW SOLVER 377
IMAGE 9
XUE CONTENTS
17.8 EXAMPLES 378
17.8.1 SPHERE IN CHANNEL (COMPRESSIBLE EULER) 378
17.8.2 SPHERE IN SHEAR FLOW (INCOMPRESSIBLE NAVIER-STOKES) 378
17.8.3 SPINNING MISSILE 379
18 EMBEDDED AND IMMERSED GRID TECHNIQUES 383
18.1 KINETIC TREATMENT OF EMBEDDED OR IMMERSED OBJECTS 385
18.1.1 IMPLEMENTATION DETAILS 388
18.2 KINEMATIC TREATMENT OF EMBEDDED SURFACES 389
18.2.1 FIRST-ORDER TREATMENT 389
18.2.2 HIGHER-ORDER TREATMENT 392
18.2.3 DETERMINATION OF CROSSED EDGES 394
18.3 DEACTIVATION OF INTERIOR REGIONS 395
18.4 EXTRAPOLATION OF THE SOLUTION 397
18.5 ADAPTIVE MESH REFINEMENT 397
18.6 LOAD/FLUX TRANSFER 398
18.7 TREATMENT OF GAPS OR CRACKS 399
18.8 DIRECT LINK TO PARTICLES 400
18.9 EXAMPLES 401
18.9.1 SODSHOCKTUBE 401
18.9.2 SHUTTLE ASCEND CONFIGURATION 401
18.9.3 BLAST INTERACTION WITH A GENERIC SHIP HUELL 402
18.9.4 GENERIC WEAPON FRAGMENTATION 404
18.9.5 FLOW PAST A SPHERE 405
18.9.6 DISPERSION IN AN INNER CITY 411
18.9.7 COMPLEX ENDOVASCULAR DEVICES 411
18.9.8 FLOW PAST A VW GOLF 5 411
19 TREATMENT OF FREE SURFACES 419
19.1 INTERFACE FITTING METHODS 419
19.1.1 FREE SURFACE DISCRETIZATION 421
19.1.2 OVERALL SCHEME 422
19.1.3 MESH UPDATE 422
19.1.4 EXAMPLES FOR SURFACE FITTING 424
19.1.5 PRACTICAL LIMITATIONS OF FREE SURFACE FITTING 427
19.2 INTERFACE CAPTURING METHODS 429
19.2.1 EXTRAPOLATION OF THE PRESSURE 432
19.2.2 EXTRAPOLATION OF THE VELOCITY 432
19.2.3 KEEPING INTERFACES SHARP 432
19.2.4 IMPOSITION OF CONSTANT MASS 433
19.2.5 DEACTIVATION OF AIR REGION 433
19.2.6 TREATMENT OFBUBBLES 434
19.2.7 ADAPTIVE REFINEMENT 435
19.2.8 EXAMPLES FOR SURFACE CAPTURING 435
19.2.9 PRACTICAL LIMITATIONS OF FREE SURFACE CAPTURING 448
IMAGE 10
CONTENTS XUEI
20 OPTIMAL SHAPE AND PROCESS DESIGN 449
20.1 THE GENERAL OPTIMIZATION PROBLEM 449
20.2 OPTIMIZATION TECHNIQUES 451
20.2.1 RECURSIVE EXHAUSTIVE PARAMETER SCOPING 452
20.2.2 GENETIC ALGORITHMS 453
20.2.3 GRADIENT-BASED ALGORITHMS 458
20.3 ADJOINT SOLVERS 462
20.3.1 ADJOINT EQUATIONS: RESIDUALS WITH FIRST DERIVATIVES AND SOURCE
TERMS . . 463 20.3.2 ADJOINT EQUATIONS: RESIDUALS WITH SECOND
DERIVATIVES 464
20.3.3 JACOBIANS FOR EULER/NAVIER-STOKES EQUATIONS 465
20.3.4 ADJOINT SOLVERS 467
20.3.5 GRADIENT EVALUATION 468
20.4 GEOMETRIE CONSTRAINTS 469
20.4.1 VOLUME CONSTRAINT VIA COST FUNETION 469
20.4.2 VOLUME CONSTRAINT VIA GRADIENT PROJEETION 470
20.4.3 VOLUME CONSTRAINT VIA POST-PROCESSING 471
20.5 APPROXIMATE GRADIENTS 471
20.6 MULTIPOINT OPTIMIZATION 471
20.7 REPRESENTATION OF SURFACE CHANGES 472
20.8 HIERARCHICAL DESIGN PROCEDURES 472
20.9 TOPOLOGICAL OPTIMIZATION VIA POROSITIES 473
20.10EXAMPLES 474
20.10.1 DAMAGE ASSESSMENT FOR CONTAMINANT RELEASE 474
20.10.2 EXTERNAL NOZZLE 475
20.10.3 WIGLEY HUELL 477
20.10.4 KRISO CONTAINER SHIP(KCS) 480
REFERENCES 481
INDEX 515 |
| adam_txt |
IMAGE 1
APPLIED
COMPUTATIONAL FLUID DYNAMICS TECHNIQUES AN INTRODUCTION BASED ON
FINITE ELEMENT METHODS
SECOND EDITION
RAINALD LOEHNER CENTER FOR COMPUTATIONAL FLUID DYNAMICS, DEPARTMENT OF
COMPUTATIONAL AND DATA SCIENCES, COLLEGE OF SCIENCES, GEORGE MASON
UNIVERSITY, FAIRFAX, VIRGINIA, USA
JOHN WILEY & SONS, LTD C
IMAGE 2
CONTENTS
FOREWORD TO THE SECOND EDITION XIV
ACKNOWLEDGEMENTS XVII
1 INTRODUCTION AND GENERAL CONSIDERATIONS 1
1.1 THE CFD CODE 4
1.2 PORTING RESEARCH CODES TO AN INDUSTRIAL CONTEXT 5
1.3 SCOPE OF THE BOOK 5
2 DATA STRUCTURES AND ALGORITHMS 7
2.1 REPRESENTATION OF A GRID 7
2.2 DERIVED DATA STRUCTURES FOR STATIC DATA 9
2.2.1 ELEMENTS SURROUNDING POINTS - LINKED LISTS 9
2.2.2 POINTS SURROUNDING POINTS 10
2.2.3 ELEMENTS SURROUNDING ELEMENTS 12
2.2.4 EDGES 14
2.2.5 EXTERNAL FACES 14
2.2.6 EDGES OF AN DEMENT 16
2.3 DERIVED DATA STRUCTURES FOR DYNAMIC DATA 17
2.3.1 N-TREES 18
2.4 SORTING AND SEARCHING 19
2.4.1 HEAP LISTS 19
2.5 PROXIMITY IN SPACE 22
2.5.1 BINS 22
2.5.2 BINARY TREES 26
2.5.3 QUADTREES AND OCTREES 28
2.6 NEAREST-NEIGHBOURS AND GRAPHS 30
2.7 DISTANCE TO SURFACE 30
3 GRID GENERATION 35
3.1 DESCRIPTION OF THE DOMAIN TO BE GRIDDED 37
3.1.1 ANALYTICAL FUNCTIONS 37
3.1.2 DISCRETEDATA 37
3.2 VARIATION OF DEMENT SIZE AND SHAPE 38
3.2.1 INTERNAL MEASURES OF GRID QUALITY 39
3.2.2 ANALYTICAL FUNCTIONS ^ 39
3.2.3 BOXES ) 39
IMAGE 3
CONTENTS
3.2.4 POINT/LINE/SURFACE SOURCES 39
3.2.5 BACKGROUND GRIDS 42
3.2.6 ELEMENT SIZE ATTACHED TO CAD DATA 43
3.2.7 ADAPTIVE BACKGROUND GRIDS 43
3.2.8 SURFACE GRIDDING WITH ADAPTIVE BACKGROUND GRIDS 45
3.3 ELEMENT TYPE 46
3.4 AUTOMATIC GRID GENERATION METHODS 47
3.5 OTHER GRID GENERATION METHODS 49
3.6 THE ADVANCING FRONT TECHNIQUE 51
3.6.1 CHECKING THE INTERSECTION OF FACES 52
3.6.2 DATA STRUCTURES TO MINIMIZE SEARCH OVERHEADS 56
3.6.3 ADDITIONAL TECHNIQUES TO INCREASE SPEED 56
3.6.4 ADDITIONAL TECHNIQUES TO ENHANCE RELIABILITY 58
3.7 DELAUNAY TRIANGULATION 59
3.7.1 CIRCUMSPHERE CALCULATIONS 61
3.7.2 DATA STRUCTURES TO MINIMIZE SEARCH OVERHEADS 62
3.7.3 BOUNDARY RECOVERY 63
3.7.4 ADDITIONAL TECHNIQUES TO INCREASE SPEED 63
3.7.5 ADDITIONAL TECHNIQUES TO ENHANCE RELIABILITY AND QUALITY 64
3.8 GRID IMPROVEMENT 65
3.8.1 REMOVAL OF BAD ELEMENTS 66
3.8.2 LAPLACIAN SMOOTHING 67
3.8.3 GRID OPTIMIZATION 67
3.8.4 SELECTIVE MESH MOVEMENT 67
3.8.5 DIAGONAL SWAPPING 68
3.9 OPTIMAL SPACE-FILLING TETRAHEDRA 70
3.10 GRIDS WITH UNIFORM CORES 72
3.11 VOLUME-TO-SURFACE MESHING 73
3.12 NAVIER-STOKES GRIDDING TECHNIQUES 75
3.12.1 DESIGN CRITERIA FOR RANS GRIDDERS 77
3.12.2 SMOOTHING OF SURFACE NORMALS 79
3.12.3 POINT DISTRIBUTION ALONG NORMALS 81
3.12.4 SUBDIVISION OF PRISMS INTO TETRAHEDRA 81
3.12.5 ELEMENT REMOVAL CRITERIA 83
3.13 FILLING SPACE WITH POINTS/ARBITRARY OBJECTS 90
3.13.1 THE ADVANCING FRONT SPACE-FILLING ALGORITHM 90
3.13.2 POINT/OBJECT PLACEMENT STENCILS 91
3.13.3 BOUNDARY CONSISTENCY CHECKS 93
3.13.4 MAXIMUM COMPACTION TECHNIQUES 93
3.13.5 ARBITRARY OBJECTS 96
3.13.6 DEPOSITION PATTERNS 96
3.14 APPLICATIONS 98
3.14.1 SPACE SHUTTLE ASCEND CONFIGURATION 99
3.14.2 PILOTEJECTINGFROMF18 100
3.14.3 CIRCLEOF WILLIS 103
3.14.4 GENERIC SUBMARINE BODY 105
IMAGE 4
V LL
3.14.5 AHMED CARBODY 105
3.14.6 TRACK 105
3.14.7 POINTCLOUDFORF117 106
3.14.8 HOPPER FUELED WITH BEANS/ELLIPSOIDS 107
3.14.9 CUBE MED WITH SPHERES OF DIFFERENT SIZES 107
4 APPROXIMATION THEORY 109
4.1 THE BASIC PROBLEM 109
4.1.1 POINT FITTING 110
4.1.2 WEIGHTED RESIDUAL METHODS 110
4.1.3 LEAST-SQUARES FORMULATION 112
4.2 CHOICE OF TRIAL FUNCTIONS 112
4.2.1 CONSTANT TRIAL FUNCTIONS IN ONE DIMENSION 112
4.2.2 LINEAR TRIAL FUNCTIONS IN ONE DIMENSION 113
4.2.3 QUADRATIC TRIAL FUNCTIONS IN ONE DIMENSION 114
4.2.4 LINEAR TRIAL FUNCTIONS IN TWO DIMENSIONS 115
4.2.5 QUADRATIC TRIAL FUNCTIONS IN TWO DIMENSIONS 117
4.3 GENERAL PROPERTIES OF SHAPE FUNCTIONS 118
4.4 WEIGHTED RESIDUAL METHODS WITH LOCAL FUNCTIONS 118
4.5 ACCURACY AND EFFORT 119
4.6 GRID ESTIMATES 121
5 APPROXIMATION OF OPERATORS 123
5.1 TAXONOMY OF METHODS 123
5.1.1 FINITE DIFFERENCE METHODS 123
5.1.2 FINITE VOLUME METHODS 124
5.1.3 GALERKIN FINITE DEMENT METHODS 124
5.1.4 PETROV-GALERKIN FINITE DEMENT METHODS 124
5.1.5 SPECTRAL DEMENT METHODS 124
5.2 THE POISSON OPERATOR 124
5.2.1 MINIMIZATION PROBLEM 125
5.2.2 AN EXAMPLE 126
5.2.3 TUTORIAL: CODE FRAGMENT FOR HEAT EQUATION 128
5.3 RECOVERY OF DERIVATIVES 130
5.3.1 FIRST DERIVATIVES 131
5.3.2 SECOND DERIVATIVES 131
5.3.3 HIGHER DERIVATIVES 132
6 DISCRETIZATION IN TIME 133
6.1 EXPLICIT SCHEMES 133
6.2 IMPLICIT SCHEMES 135
6.2.1 SITUATIONS WHERE IMPLICIT SCHEMES PAY OFF 136
6.3 A WORD OF CAUTION 136
IMAGE 5
V L LL
CONTENTS
7 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 137
7.1 DIRECT SOLVERS 137
7.1.1 GAUSSIAN ELIMINATION 137
7.1.2 CROUT ELIMINATION 139
7.1.3 CHOLESKY ELIMINATION 140
7.2 ITERATIVE SOLVERS 140
7.2.1 MATRIX PRECONDITIONING 141
7.2.2 GLOBALIZATION PROCEDURES 147
7.3 MULTIGRID METHODS 153
7.3.1 THE MULTIGRID CONCEPT 154
7.3.2 INJECTION AND PROJECTION OPERATORS 155
7.3.3 GRIDCYCLING 157
7.3.4 ALGORITHMIC COMPLEXITY AND STORAGE REQUIREMENTS 157
7.3.5 SMOOTHING 158
7.3.6 AN EXAMPLE 159
8 SIMPLE EULER/NAVIER-STOKES SOLVERS 161
8.1 GALERKIN APPROXIMATION 162
8.1.1 EQUIVALENCY WITH FVM 164
8.2 LAX-WENDROFF(TAYLOR-GALERKIN) 164
8.2.1 EXPEDITING THE RHS EVALUATION 165
8.2.2 LINEAR ELEMENTS (TRIANGLES, TETRAHEDRA) 166
8.3 SOLVING FOR THE CONSISTENT MASS MATRIX 167
8.4 ARTIFICIAL VISCOSITIES 167
8.5 BOUNDARY CONDITIONS 169
8.6 VISCOUS FLUXES 172
9 FLUX-CORRECTED TRANSPORT SCHEMES 175
9.1 ALGORITHMIC IMPLEMENTATION 176
9.1.1 THE LIMITING PROCEDURE 176
9.2 STEEPENING 178
9.3 FCT FOR TAYLOR-GALERKIN SCHEMES 179
9.4 ITERATIVE LIMITING 179
9.5 LIMITING FOR SYSTEMS OF EQUATIONS 180
9.5.1 LIMITING ANY SET OF QUANTITIES 180
9.6 EXAMPLES 181
9.6.1 SHOCKTUBE 181
9.6.2 SHOCK DIFFRACTION OVER A WALL 182
9.7 SUMMARY 183
10 EDGE-BASED COMPRESSIBLE FLOW SOLVERS 187
10.1 THE LAPLACIAN OPERATOR 188
10.2 FIRST DERIVATIVES: FIRST FORM 190
10.3 FIRST DERIVATIVES: SECOND FORM 191
10.4 EDGE-BASED SCHEMES FOR ADVECTION-DOMINATED PDES 193
10.4.1 EXACT RIEMANN SOLVER (GODUNOV SCHEME) 194
10.4.2 APPROXIMATE RIEMANN SOLVERS 195
IMAGE 6
IX
10.4.3 SCALAR LIMITED DISSIPATION 197
10.4.4 SCALAR DISSIPATION WITH PRESSURE SENSORS 197
10.4.5 SCALAR DISSIPATION WITHOUT GRADIENTS 198
10.4.6 TAYLOR-GALERKIN SCHEMES 199
10.4.7 FLUX-CORRECTED TRANSPORT SCHEMES 199
11 INCOMPRESSIBLE FLOW SOLVERS 201
11.1 THE ADVECTION OPERATOR 201
11.1.1 INTEGRATION ALONG CHARACTERISTICS 202
11.1.2 TAYLOR-GALERKIN 202
11.1.3 EDGE-BASED UPWINDING 203
11.2 THE DIVERGENCE OPERATOR 203
11.3 ARTIFICIAL COMPRESSIBILITY 206
11.4 TEMPORAL DISCRETIZATION: PROJECTION SCHEMES 206
11.5 TEMPORAL DISCRETIZATION: IMPLICIT SCHEMES 208
11.6 TEMPORAL DISCRETIZATION OF HIGHER ORDER 209
11.7 ACCELERATION TO THE STEADY STATE 210
11.7.1 LOCAL TIMESTEPPING 210
11.7.2 REDUCED PRESSURE ITERATIONS 210
11.7.3 SUBSTEPPING FOR THE ADVECTION TERMS 211
11.7.4 IMPLICIT TREATMENT OF THE ADVECTION TERMS 211
11.8 PROJECTIVE PREDICTIONOF PRESSURE INCREMENTS 212
11.9 EXAMPLES 213
11.9.1 VON KARMAN VORTEX STREET 213
11.9.2 NACA0012WING 216
11.9.3 LPD-17TOPSIDE FLOW STUDY 218
11.9.4 DARPA SUBOFF MODEL 223
11.9.5 GENERIC SUBMARINE FOREBODY VORTEX FLOW STUDY 225
12 MESH MOVEMENT 227
12.1 THE ALE FRAME OF REFERENCE 227
12.1.1 BOUNDARY CONDITIONS 228
12.2 GEOMETRIE CONSERVATION LAW 228
12.3 MESH MOVEMENT ALGORITHMS 229
12.3.1 SMOOTHINGOFTHEVELOCITYFIELD 230
12.3.2 SMOOTHING OF THE COORDINATES 233
12.3.3 PRESCRIPTION VIA ANALYTIC FUNETIONS 235
12.4 REGION OF MOVING ELEMENTS 235
12.5 PDE-BASED DISTANCE FUNETIONS 236
12.5.1 EIKONAL EQUATION 237
12.5.2 LAPLACE EQUATION 237
12.6 PENALIZATION OF DEFORMED ELEMENTS 238
12.7 SPECIAL MOVEMENT TECHNIQUES FOR RANS GRIDS 239
12.8 ROTATING PARTS/DOMAINS 240
IMAGE 7
X CONTENTS
12.9 APPLICATIONS 241
12.9.1 MULTIPLE SPHERES 241
12.9.2 PILOTEJECTIONFROMF18 242
12.9.3 DRIFTING FLEET OF SHIPS 242
13 INTERPOLATION 245
13.1 BASIC INTERPOLATION ALGORITHM 246
13.2 FASTEST 1-TIME ALGORITHM: BRUETE FORCE 247
13.3 FASTEST IV-TIME ALGORITHM: OCTREE SEARCH 247
13.4 FASTEST KNOWN VICINITY ALGORITHM: NEIGHBOUR-TO-NEIGHBOUR 249
13.5 FASTEST GRID-TO-GRID ALGORITHM: ADVANCING-FRONT VICINITY 250
13.5.1 LAYERING OF BRUTE-FORCE SEARCHES 252
13.5.2 INSIDE-OUT INTERPOLATION 253
13.5.3 MEASURING CONCAVITY 253
13.5.4 VECTORIZATION 254
13.6 CONSERVATIVE INTERPOLATION 257
13.6.1 CONSERVATIVE AND MONOTONIC INTERPOLATION 259
13.7 SURFACE-GRID-TO-SURFACE-GRID INTERPOLATION 261
13.8 PARTICLE-GRID INTERPOLATION 265
14 ADAPTIVE MESH REFINEMENT 269
14.1 OPTIMAL-MESH CRITERIA 270
14.2 ERROR INDICATORS/ESTIMATORS 271
14.2.1 ERROR INDICATORS COMMONLY USED 272
14.2.2 PROBLEMS WITH MULTIPLE SCALES 275
14.2.3 DETERMINATION OF ELEMENT SIZE AND SHAPE 276
14.3 REFINEMENT STRATEGIES 278
14.3.1 MESH MOVEMENT OR REPOSITIONING (R-METHODS) 278
14.3.2 MESH ENRICHMENT (H/P-METHODS) 278
14.3.3 ADAPTIVE REMESHING (M-METHODS) 284
14.3.4 COMBINATIONS 286
14.4 TUTORIAL: H-REFINEMENT WITH TETRAHEDRA 286
14.4.1 ALGORITHMIC IMPLEMENTATION 287
14.5 EXAMPLES 291
14.5.1 CONVECTION BETWEEN CONCENTRIC CYLINDERS 291
14.5.2 SHOCK-OBJECT INTERACTION IN TWO DIMENSIONS 294
14.5.3 SHOCK-OBJECT INTERACTION IN THREE DIMENSIONS 296
14.5.4 SHOCK-STRUCTURE INTERACTION 297
14.5.5 OBJECT FALLING INTO SUPERSONIC FREE STREAM TWO DIMENSIONS 297
15 EFFICIENT USE OF COMPUTER HARDWARE 299
15.1 REDUCTION OF CACHE-MISSES 300
15.1.1 ARRAY ACCESS IN LOOPS 300
15.1.2 POINT RENUMBERING 301
15.1.3 REORDERING OF NODES WITHIN ELEMENTS 306
15.1.4 RENUMBERING OF EDGES ACCORDING TO POINTS 306
IMAGE 8
CONTENTS XI
15.1.5 SOME TIMINGS 308
15.1.6 AGGLOMERATION TECHNIQUES 309
15.2 VECTOR MACHINES 316
15.2.1 BASIC EDGE COLOURING ALGORITHM 317
15.2.2 BACKWARD/FORWARD STRATEGY 318
15.2.3 COMBINING VECTORIZABILITY WITH DATA LOCALITY 318
15.2.4 SWITCHING ALGORITHM 319
15.2.5 REDUCED I/A LOOPS 321
15.2.6 ALTERNATIVE RHS FORMATION 326
15.3 PARALLEL MACHINES: GENERAL CONSIDERATIONS 328
15.4 SHARED-MEMORY PARALLEL MACHINES 329
15.4.1 LOCAL AGGLOMERATION 330
15.4.2 GLOBAL AGGLOMERATION 331
15.4.3 IMPLEMENTATIONAL ISSUES 333
15.5 SIMD MACHINES 334
15.6 MIMD MACHINES 336
15.6.1 GENERAL CONSIDERATIONS 337
15.6.2 LOAD BALANCING AND DOMAIN SPLITTING 337
15.6.3 PARALLEL FLOW SOLVERS 342
15.7 THE EFFECT OFMOORE'S LAW ON PARALLEL COMPUTING 344
15.7.1 THE LIFE CYCLE OF SCIENTIFIC COMPUTING CODES 346
15.7.2 EXAMPLES 348
15.7.3 THE CONSEQUENCES OFMOORE'S LAW 349
16 SPACE-MARCHING AND DEACTIVATION 351
16.1 SPACE-MARCHING 351
16.1.1 MASKING OF POINTS AND EDGES 352
16.1.2 RENUMBERING OF POINTS AND EDGES 354
16.1.3 GROUPING TO AVOID MEMORY CONTENTION 355
16.1.4 EXTRAPOLATION OF THE SOLUTION 356
16.1.5 TREATMENT OF SUBSONIC POCKETS 357
16.1.6 MEASURING CONVERGENCE 357
16.1.7 APPLICATION TO TRANSIENT PROBLEMS 358
16.1.8 MACRO-BLOCKING 359
16.1.9 EXAMPLES FOR SPACE-MARCHING AND BLOCKING 360
16.2 DEACTIVATION 365
16.2.1 EXAMPLES OF DYNAMIC DEACTIVATION 366
17 OVERLAPPING GRIDS 371
17.1 INTERPOLATION CRITERIA 372
17.2 EXTERNAL BOUNDARIES AND DOMAINS 373
17.3 INTERPOLATION: INITIALIZATION 373
17.4 TREATMENT OF DOMAINS THAT ARE PARTIALLY OUTSIDE 375
17.5 REMOVAL OF INACTIVE REGIONS 375
17.6 INCREMENTAL INTERPOLATION 377
17.7 CHANGES TO THE FLOW SOLVER 377
IMAGE 9
XUE CONTENTS
17.8 EXAMPLES 378
17.8.1 SPHERE IN CHANNEL (COMPRESSIBLE EULER) 378
17.8.2 SPHERE IN SHEAR FLOW (INCOMPRESSIBLE NAVIER-STOKES) 378
17.8.3 SPINNING MISSILE 379
18 EMBEDDED AND IMMERSED GRID TECHNIQUES 383
18.1 KINETIC TREATMENT OF EMBEDDED OR IMMERSED OBJECTS 385
18.1.1 IMPLEMENTATION DETAILS 388
18.2 KINEMATIC TREATMENT OF EMBEDDED SURFACES 389
18.2.1 FIRST-ORDER TREATMENT 389
18.2.2 HIGHER-ORDER TREATMENT 392
18.2.3 DETERMINATION OF CROSSED EDGES 394
18.3 DEACTIVATION OF INTERIOR REGIONS 395
18.4 EXTRAPOLATION OF THE SOLUTION 397
18.5 ADAPTIVE MESH REFINEMENT 397
18.6 LOAD/FLUX TRANSFER 398
18.7 TREATMENT OF GAPS OR CRACKS 399
18.8 DIRECT LINK TO PARTICLES 400
18.9 EXAMPLES 401
18.9.1 SODSHOCKTUBE 401
18.9.2 SHUTTLE ASCEND CONFIGURATION 401
18.9.3 BLAST INTERACTION WITH A GENERIC SHIP HUELL 402
18.9.4 GENERIC WEAPON FRAGMENTATION 404
18.9.5 FLOW PAST A SPHERE 405
18.9.6 DISPERSION IN AN INNER CITY 411
18.9.7 COMPLEX ENDOVASCULAR DEVICES 411
18.9.8 FLOW PAST A VW GOLF 5 411
19 TREATMENT OF FREE SURFACES 419
19.1 INTERFACE FITTING METHODS 419
19.1.1 FREE SURFACE DISCRETIZATION 421
19.1.2 OVERALL SCHEME 422
19.1.3 MESH UPDATE 422
19.1.4 EXAMPLES FOR SURFACE FITTING 424
19.1.5 PRACTICAL LIMITATIONS OF FREE SURFACE FITTING 427
19.2 INTERFACE CAPTURING METHODS 429
19.2.1 EXTRAPOLATION OF THE PRESSURE 432
19.2.2 EXTRAPOLATION OF THE VELOCITY 432
19.2.3 KEEPING INTERFACES SHARP 432
19.2.4 IMPOSITION OF CONSTANT MASS 433
19.2.5 DEACTIVATION OF AIR REGION 433
19.2.6 TREATMENT OFBUBBLES 434
19.2.7 ADAPTIVE REFINEMENT 435
19.2.8 EXAMPLES FOR SURFACE CAPTURING 435
19.2.9 PRACTICAL LIMITATIONS OF FREE SURFACE CAPTURING 448
IMAGE 10
CONTENTS XUEI
20 OPTIMAL SHAPE AND PROCESS DESIGN 449
20.1 THE GENERAL OPTIMIZATION PROBLEM 449
20.2 OPTIMIZATION TECHNIQUES 451
20.2.1 RECURSIVE EXHAUSTIVE PARAMETER SCOPING 452
20.2.2 GENETIC ALGORITHMS 453
20.2.3 GRADIENT-BASED ALGORITHMS 458
20.3 ADJOINT SOLVERS 462
20.3.1 ADJOINT EQUATIONS: RESIDUALS WITH FIRST DERIVATIVES AND SOURCE
TERMS . . 463 20.3.2 ADJOINT EQUATIONS: RESIDUALS WITH SECOND
DERIVATIVES 464
20.3.3 JACOBIANS FOR EULER/NAVIER-STOKES EQUATIONS 465
20.3.4 ADJOINT SOLVERS 467
20.3.5 GRADIENT EVALUATION 468
20.4 GEOMETRIE CONSTRAINTS 469
20.4.1 VOLUME CONSTRAINT VIA COST FUNETION 469
20.4.2 VOLUME CONSTRAINT VIA GRADIENT PROJEETION 470
20.4.3 VOLUME CONSTRAINT VIA POST-PROCESSING 471
20.5 APPROXIMATE GRADIENTS 471
20.6 MULTIPOINT OPTIMIZATION 471
20.7 REPRESENTATION OF SURFACE CHANGES 472
20.8 HIERARCHICAL DESIGN PROCEDURES 472
20.9 TOPOLOGICAL OPTIMIZATION VIA POROSITIES 473
20.10EXAMPLES 474
20.10.1 DAMAGE ASSESSMENT FOR CONTAMINANT RELEASE 474
20.10.2 EXTERNAL NOZZLE 475
20.10.3 WIGLEY HUELL 477
20.10.4 KRISO CONTAINER SHIP(KCS) 480
REFERENCES 481
INDEX 515 |
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| author | Löhner, Rainald |
| author_facet | Löhner, Rainald |
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| bvnumber | BV023089753 |
| callnumber-first | T - Technology |
| callnumber-label | TA357 |
| callnumber-raw | TA357 |
| callnumber-search | TA357 |
| callnumber-sort | TA 3357 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UF 4000 UF 4050 |
| classification_tum | MTA 309f MAT 674f |
| ctrlnum | (OCoLC)180471214 (DE-599)BVBBV023089753 |
| dewey-full | 620.1/064 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
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| dewey-raw | 620.1/064 |
| dewey-search | 620.1/064 |
| dewey-sort | 3620.1 264 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023089753 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:40:29Z |
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| institution | BVB |
| isbn | 047051907X 9780470519073 |
| language | English |
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| oclc_num | 180471214 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-634 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-29T DE-634 DE-91G DE-BY-TUM |
| physical | XVIII, 519 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| spelling | Löhner, Rainald Verfasser aut Applied computational fluid dynamics techniques an introduction based on finite element methods Rainald Löhner Applied CFD techniques 2. ed. Chichester [u.a.] Wiley 2008 XVIII, 519 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nebentitel: Applied CFD techniques Mathematik Finite element method Fluid dynamics Mathematics Numerical analysis 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://deposit.dnb.de/cgi-bin/dokserv?id=3035971&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016292637&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Löhner, Rainald Applied computational fluid dynamics techniques an introduction based on finite element methods Mathematik Finite element method Fluid dynamics Mathematics Numerical analysis 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 | Applied computational fluid dynamics techniques an introduction based on finite element methods |
| title_alt | Applied CFD techniques |
| title_auth | Applied computational fluid dynamics techniques an introduction based on finite element methods |
| title_exact_search | Applied computational fluid dynamics techniques an introduction based on finite element methods |
| title_exact_search_txtP | Applied computational fluid dynamics techniques an introduction based on finite element methods |
| title_full | Applied computational fluid dynamics techniques an introduction based on finite element methods Rainald Löhner |
| title_fullStr | Applied computational fluid dynamics techniques an introduction based on finite element methods Rainald Löhner |
| title_full_unstemmed | Applied computational fluid dynamics techniques an introduction based on finite element methods Rainald Löhner |
| title_short | Applied computational fluid dynamics techniques |
| title_sort | applied computational fluid dynamics techniques an introduction based on finite element methods |
| title_sub | an introduction based on finite element methods |
| topic | Mathematik Finite element method Fluid dynamics Mathematics Numerical analysis Numerische Strömungssimulation (DE-588)4690080-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Mathematik Finite element method Fluid dynamics Mathematics Numerical analysis Numerische Strömungssimulation Finite-Elemente-Methode |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3035971&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016292637&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lohnerrainald appliedcomputationalfluiddynamicstechniquesanintroductionbasedonfiniteelementmethods AT lohnerrainald appliedcfdtechniques |