Random fields and stochastic Lagrangian models: analysis and applications in turbulence and porous media
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2013
|
| Subjects: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=4097380&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=025955619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. |
| Physical Description: | XV, 399 S. graph. Darst. |
| ISBN: | 9783110296648 |
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| 100 | 1 | |a Sabel'fel'd, Karl K. |d 1953- |e Verfasser |0 (DE-588)121181529 |4 aut | |
| 245 | 1 | 0 | |a Random fields and stochastic Lagrangian models |b analysis and applications in turbulence and porous media |c Karl K. Sabelfeld |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2013 | |
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| adam_text | IMAGE 1
CONTENTS
PREFACE V
1 INTRODUCTION 1
1.1 WHY RANDOM FIELDS? 1
1.2 SOME EXAMPLES 3
1.3 FUNDAMENTAL CONCEPTS 8
1.3.1 RANDOM FUNCTIONS IN A BROAD SENSE 9
1.3.2 GAUSSIAN RANDOM VECTORS 13
1.3.3 GAUSSIAN RANDOM FUNCTIONS 14
1.3.4 RANDOM FIELDS 16
1.3.5 STOCHASTIC MEASURES AND INTEGRALS 17
1.3.6 INTEGRAL REPRESENTATION O F RANDOM FUNCTIONS 19
1.3.7 RANDOM TRAJECTORIES 21
1.3.8 STOCHASTIC DIFFERENTIAL, ITO INTEGRALS 22
1.3.9 BROWNIAN MOTION 22
1.3.10 MULTIDIMENSIONAL DIFFUSION AND FOKKER-PLANCK EQUATION . . . . 25
1.3.11 CENTRAL LIMIT THEOREM AND CONVERGENCE O F A POISSON PROCESS TO
A GAUSSIAN PROCESS 26
2 STOCHASTIC SIMULATION O F VECTOR GAUSSIAN RANDOM FIELDS 29
2.1 INTRODUCTION 29
2.2 DISCRETE EXPANSIONS RELATED TO THE SPECTRAL REPRESENTATIONS OF
GAUSSIAN
RANDOM FIELDS 30
2.2.1 SPECTRAL REPRESENTATIONS 30
2.2.2 SERIES EXPANSIONS 31
2.2.3 EXPANSION WITH AN EVEN COMPLEX ORTHONORMAL SYSTEM 31
2.2.4 EXPANSION WITH A REAL ORTHONORMAL SYSTEM 32
2.2.5 COMPLEX VALUED ORTHOGONAL EXPANSIONS 33
2.3 WAVELET EXPANSIONS 33
2.3.1 FOURIER WAVELET EXPANSIONS 34
HTTP://D-NB.INFO/1024907201
IMAGE 2
VIII CONTENTS
2.3.2 WAVELET EXPANSION 35
2.3.3 MOVING AVERAGES 36
2.4 RANDOMIZED SPECTRAL MODELS 37
2.4.1 RANDOMIZED SPECTRAL MODELS DEFINED THROUGH STOCHASTIC
INTEGRALS 37
2.4.2 STRATIFIED RSM FOR HOMOGENEOUS RANDOM FIELDS 39
2.5 FOURIER WAVELET MODELS 39
2.5.1 MEYER WAVELET FUNCTIONS 40
2.5.2 EVALUATION O F THE COEFFICIENTS 3 R ^ AND 40
2.5.3 CUT-OFF PARAMETERS 4 2
2.5.4 CHOICE O F PARAMETERS 43
2.6 FOURIER WAVELET MODELS O F HOMOGENEOUS RANDOM FIELDS BASED ON
RANDOMIZATION O F PLANE WAVE DECOMPOSITION 47
2.6.1 PLANE WAVE DECOMPOSITION O F HOMOGENEOUS RANDOM FIELDS . . . 47
2.6.2 DECOMPOSITION WITH FIXED NODES 50
2.6.3 DECOMPOSITION WITH RANDOMLY DISTRIBUTED NODES 52
2.6.4 SOME EXAMPLES 54
2.6.5 FLOW IN A POROUS MEDIA IN THE FIRST ORDER APPROXIMATION 56
2.6.6 FOURIER WAVELET MODELS O F GAUSSIAN RANDOM FIELDS 57
2.7 COMPARISON O F FOURIER WAVELET AND RANDOMIZED SPECTRAL MODELS 58
2.7.1 SOME TECHNICAL DETAILS O F RSM 58
2.7.2 SOME TECHNICAL DETAILS O F FWM 60
2.7.3 ENSEMBLE AVERAGING 62
2.7.4 SPACE AVERAGING 62
2.8 CONCLUSIONS 63
2.9 APPENDICES 65
2.9.1 APPENDIX A. POSITIVE DEFINITENESS O F THE MATRIX 35 65
2.9.2 APPENDIX B. PROOF O F PROPOSITION 2.1 65
3 STOCHASTIC LAGRANGIAN MODELS O F TURBULENT FLOWS: RELATIVE DISPERSION
OF
A PAIR O F FLUID PARTICLES 70
3.1 INTRODUCTION 70
3.2 CRITICISM O F 2-PARTICLE MODELS 73
IMAGE 3
CONTENTS IX
3.3 THE QUASI-L-DIMENSIONAL LAGRANGIAN MODEL O F RELATIVE DISPERSION . .
. . 77
3.3.1 QUASI-L-DIMENSIONAL ANALOG O F FORMULA (2.14A) 78
3.3.2 MODELS WITH A FINITE-ORDER CONSISTENCY 80
3.3.3 EXPLICIT FORM O F THE MODEL (3.26, 3.27) 83
3.3.4 EXAMPLE 88
3.4 A 3-DIMENSIONAL MODEL O F RELATIVE DISPERSION 90
3.5 LAGRANGIAN MODELS CONSISTENT WITH THE EULERIAN STATISTICS 92
3.5.1 DIFFUSION APPROXIMATION 92
3.5.2 RELATION TO THE WELL-MIXED CONDITION 94
3.5.3 A CHOICE O F THE COEFFICIENTS A,- AND BIJ 95
3.6 CONCLUSIONS 97
4 A NEW LAGRANGIAN MODEL O F 2-PARTICLE RELATIVE TURBULENT DISPERSION 98
4.1 INTRODUCTION 98
4.2 AN EXAMINATION O F DURBIN S NONLINEAR MODEL 98
4.3 MATHEMATICAL FORMULATION OF A NEW MODEL 100
4.4 A QUALITATIVE ANALYSIS O F THE PROBLEM (4.14) FOR SYMMETRIC ( R )
102
4.4.1 ANALYSIS O F THE PROBLEM (4.14) IN THE DETERMINISTIC CASE 102
4.4.2 ANALYSIS O F THE PROBLEM (4.14) FOR STOCHASTIC ( R ) 103
4.5 QUALITATIVE ANALYSIS O F THE PROBLEM (4.14) IN THE GENERAL CASE 108
5 THE COMBINED EULERIAN-LAGRANGIAN MODEL 113
5.1 INTRODUCTION 113
5.2 2-PARTICLE MODELS 117
5.2.1 EULERIAN STOCHASTIC MODELS O F HIGH-REYNOLDS-NUMBER
PSEUDOTURBULENCE 117
5.3 A NEW 2-PARTICLE EULERIAN-LAGRANGIAN STOCHASTIC MODEL 120
5.3.1 FORMULATION O F 2-PARTICLE EULERIAN-LAGRANGIAN MODEL 120
5.3.2 MODELS FOR THE P. D. F. O F THE EULERIAN RELATIVE VELOCITY 123
5.4 APPENDIX 125
6 STOCHASTIC LAGRANGIAN MODELS FOR 2-PARTICLE RELATIVE DISPERSION IN
HIGH-REYNOLDS-NUMBER TURBULENCE 129
6.1 INTRODUCTION 129
IMAGE 4
X
CONTENTS
6.2 PRELIMINARIES 130
6.3 A CLOSURE O F THE QUASI-L-DIMENSIONAL MODEL O F RELATIVE DISPERSION
. . . 131
6.4 CHOICE OF THE MODEL (6.1) FOR ISOTROPIC TURBULENCE 132
6.5 THE MODEL O F RELATIVE DISPERSION O F TWO PARTICLES IN A LOCALLY
ISOTROPIC
TURBULENCE 135
6.5.1 SPECIFICATION O F THE MODEL 135
6.5.2 NUMERICAL ANALYSIS O F THE QLD-MODEL (6.30) 137
6.6 MODEL OF THE RELATIVE DISPERSION IN INTERMITTENT LOCALLY ISOTROPIC
TURBULENCE 139
6.7 CONCLUSIONS 141
7 STOCHASTIC LAGRANGIAN MODELS FOR 2-PARTICLE MOTION IN TURBULENT FLOWS.
NUMERICAL RESULTS 142
7.1 INTRODUCTION 142
7.2 CLASSICAL PSEUDOTURBULENCE MODEL 143
7.2.1 RANDOMIZED MODEL O F CLASSICAL PSEUDOTURBULENCE 143
7.2.2 MEAN SQUARE SEPARATION O F TWO PARTICLES IN CLASSICAL
PSEUDOTURBULENCE 146
7.3 CALCULATIONS BY THE COMBINED EULERIAN-LAGRANGIAN STOCHASTIC MODEL
149
7.3.1 MEAN SQUARE SEPARATION O F TWO PARTICLES 149
7.3.2 THOMSON S TWO-TO-ONE REDUCTION PRINCIPLE 152
7.3.3 CONCENTRATION FLUCTUATIONS 154
7.4 TECHNICAL REMARKS 156
7.5 CONCLUSION 158
8 THE 1-PARTICLE STOCHASTIC LAGRANGIAN MODEL FOR TURBULENT DISPERSION IN
HORIZONTALLY HOMOGENEOUS TURBULENCE 159
8.1 INTRODUCTION 159
8.2 CHOICE OF THE COEFFICIENTS IN THE ITO EQUATION 162
8.3 2D STOCHASTIC MODEL WITH GAUSSIAN P. D. F 164
8.4 NUMERICAL EXPERIMENTS 167
9 DIRECT AND ADJOINT MONTE CARLO FOR THE FOOTPRINT PROBLEM 171
9.1 INTRODUCTION 171
IMAGE 5
CONTENTS XI
9.2 FORMULATION O F THE PROBLEM 172
9.3 STOCHASTIC LAGRANGIAN ALGORITHM 173
9.3.1 DIRECT MONTE CARLO ALGORITHM 174
9.3.2 ADJOINT ALGORITHM 176
9.4 IMPENETRABLE BOUNDARY 178
9.5 REACTING SPECIES 180
9.6 NUMERICAL SIMULATIONS 183
9.7 CONCLUSION 187
9.8 APPENDICES 188
9.8.1 APPENDIX A. FLUX REPRESENTATION 188
9.8.2 APPENDIX B. PROBABILISTIC REPRESENTATION 188
9.8.3 APPENDIX C. FORWARD AND BACKWARD TRAJECTORY ESTIMATORS . . . . 189
10 LAGRANGIAN STOCHASTIC MODELS FOR TURBULENT DISPERSION IN AN
ATMOSPHERIC BOUNDARY LAYER 193
10.1 INTRODUCTION 193
10.2 NEUTRALLY STRATIFIED BOUNDARY LAYER 197
10.2.1 GENERAL CASE O F EULERIAN P. D. F 197
10.2.2 GAUSSIAN P. D. F 200
10.3 COMPARISON WITH OTHER MODELS AND MEASUREMENTS 201
10.3.1 COMPARISON WITH MEASUREMENTS IN AN IDEALLY-NEUTRAL SURFACE
LAYER (INSL) 201
10.3.2 COMPARISON WITH THE WIND TUNNEL EXPERIMENT BY RAUPACH AND
LEGG (1983) 204
10.4 CONVECTIVE CASE 207
10.5 BOUNDARY CONDITIONS 211
10.6 CONCLUSION 212
10.7 APPENDICES 213
10.7.1 APPENDIX A. DERIVATION OF THE COEFFICIENTS IN THE GAUSSIAN
CASE 213
10.7.2 APPENDIX B. RELATION TO OTHER MODELS 215
IMAGE 6
XII
CONTENTS
11 ANALYSIS O F THE RELATIVE DISPERSION O F TWO PARTICLES BY LAGRANGIAN
STOCHASTIC MODELS AND DNS METHODS 218
11.1 INTRODUCTION 218
11.2 BASIC ASSUMPTIONS 220
11.2.1 MARKOV ASSUMPTION 221
11.2.2 CONSISTENCY WITH THE SECOND KOLMOGOROV SIMILARITY
HYPOTHESIS 221
11.2.3 THOMSON S WELL-MIXED CONDITION 222
11.3 WELL-MIXED LAGRANGIAN STOCHASTIC MODELS 222
11.3.1 QUADRATIC-FORM MODELS 223
11.3.2 QUASI-L-DIMENSIONAL MODELS 224
11.3.3 3-DIMENSIONAL EXTENSION O F Q1D MODELS 225
11.4 STOCHASTIC LAGRANGIAN MODELS BASED ON THE MOMENTS APPROXIMATION
METHOD 226
11.4.1 MOMENTS APPROXIMATION CONDITIONS 226
11.4.2 REALIZABILITY O F LS MODELS BASED ON THE MOMENTS
APPROXIMATION METHOD 227
11.5 COMPARISON OF DIFFERENT MODELS O F RELATIVE DISPERSION FOR THE
INERTIAL
SUBRANGE O F A FULLY DEVELOPED TURBULENCE 229
11.5.1 Q1D QUADRATIC-FORM MODEL O F BORGAS AND YEUNG 229
11.5.2 COMPARISON O F DIFFERENT MODELS IN THE INERTIAL SUBRANGE 231
11.6 COMPARISON O F DIFFERENT Q1D MODELS O F RELATIVE DISPERSION FOR
MODESTLY LARGE REYNOLDS NUMBER TURBULENCE ( R E - 240) 232
11.6.1 PARAMETRIZATION OF EULERIAN STATISTICS 232
11.6.2 BI-GAUSSIAN P. D. F 234
11.6.3 Q1D QUADRATIC-FORM MODEL 236
12 EVALUATION O F MEAN CONCENTRATION AND FLUXES IN TURBULENT FLOWS BY
LAGRANGIAN STOCHASTIC MODELS 238
12.1 INTRODUCTION 238
12.2 FORMULATION O F THE PROBLEM 239
12.3 MONTE CARLO ESTIMATORS FOR THE MEAN CONCENTRATION AND FLUXES 243
12.3.1 FORWARD ESTIMATOR 244
IMAGE 7
CONTENTS XIII
12.3.2 MODIFIED FORWARD ESTIMATORS IN CASE O F HORIZONTALLY
HOMOGENEOUS TURBULENCE 245
12.3.3 BACKWARD ESTIMATOR 250
12.4 APPLICATION TO THE FOOTPRINT PROBLEM 251
12.5 CONCLUSION 253
12.6 APPENDICES 253
12.6.1 APPENDIX A. REPRESENTATION O F CONCENTRATION IN LAGRANGIAN
DESCRIPTION 253
12.6.2 APPENDIX B. RELATION BETWEEN FORWARD AND BACKWARD
TRANSITION DENSITY FUNCTIONS 255
12.6.3 APPENDIX C. DERIVATION O F THE RELATION BETWEEN THE FORWARD
AND BACKWARD DENSITIES 255
13 STOCHASTIC LAGRANGIAN FOOTPRINT CALCULATIONS OVER A SURFACE WITH AN
ABRUPT CHANGE O F ROUGHNESS HEIGHT 258
13.1 INTRODUCTION 258
13.2 THE GOVERNING EQUATIONS 259
13.2.1 EVALUATION O F FOOTPRINT FUNCTIONS 260
13.3 RESULTS 263
13.3.1 FOOTPRINT FUNCTIONS O F CONCENTRATION AND FLUX 263
13.4 DISCUSSION AND CONCLUSIONS 276
13.5 APPENDICES 277
13.5.1 APPENDIX A. DIMENSIONLESS MEAN-FLOW EQUATIONS 277
13.5.2 APPENDIX B. LAGRANGIAN STOCHASTIC TRAJECTORY MODEL 278
14 STOCHASTIC FLOW SIMULATION IN 3D POROUS MEDIA 280
14.1 INTRODUCTION 280
14.2 FORMULATION O F THE PROBLEM 283
14.3 DIRECT NUMERICAL SIMULATION METHOD: DSM-SOR 284
14.4 RANDOMIZED SPECTRAL MODEL (RSM) 286
14.5 TESTING THE SIMULATION PROCEDURE 288
14.6 EVALUATION OF EULERIAN AND LAGRANGIAN STATISTICAL CHARACTERISTICS
BY THE
DNS-SOR METHOD 292
14.6.1 EULERIAN STATISTICAL CHARACTERISTICS 292
IMAGE 8
XIV CONTENTS
14.6.2 LAGRANGIAN STATISTICAL CHARACTERISTICS 294
14.7 CONCLUSIONS AND DISCUSSION 298
15 A LAGRANGIAN STOCHASTIC MODEL FOR THE TRANSPORT IN STATISTICALLY
HOMOGENEOUS POROUS MEDIA 300
15.1 INTRODUCTION 300
15.2 DIRECT SIMULATION METHOD 301
15.2.1 RANDOM FLOW MODEL 301
15.2.2 NUMERICAL SIMULATION 303
15.2.3 EVALUATION O F EULERIAN CHARACTERISTICS 306
15.2.4 EVALUATION O F LAGRANGIAN CHARACTERISTICS 310
15.3 CONSTRUCTION O F THE LANGEVIN-TYPE MODEL 314
15.3.1 INTRODUCTION 314
15.3.2 LANGEVIN MODEL FOR AN ISOTROPIC POROUS MEDIUM 316
15.3.3 EXPRESSIONS O F THE DRIFT TERMS 319
15.4 NUMERICAL RESULTS AND COMPARISON AGAINST THE DSM 321
15.5 CONCLUSIONS 321
16 COAGULATION O F AEROSOL PARTICLES IN INTERMITTENT TURBULENT FLOWS 326
16.1 INTRODUCTION 326
16.2 ANALYSIS O F THE FLUCTUATIONS IN THE SIZE SPECTRUM 329
16.3 MODELS O F THE ENERGY DISSIPATION RATE 332
16.3.1 THE MODEL BY POPE AND CHEN (P&CH) 332
16.3.2 THE MODEL BY BORGAS AND SAWFORD (B&S) 334
16.4 MONTE CARLO SIMULATION FOR THE SMOLUCHOWSKI EQUATION IN A
STOCHASTIC
COAGULATION REGIME 335
16.4.1 THE TOTAL NUMBER O F CLUSTERS AND THE MEAN CLUSTER SIZE 337
16.4.2 THE FUNCTIONS N^{T) AND N O(T) 339
16.4.3 THE SIZE SPECTRUM FOR DIFFERENT TIME INSTANCES 340
16.4.4 COMPARATIVE ANALYSIS FOR TWO DIFFERENT MODELS O F THE ENERGY
DISSIPATION RATE 341
16.5 THE CASE O F A COAGULATION COEFFICIENT WITH NO DEPENDENCE ON THE
CLUSTER SIZE 342
16.6 SIMULATION O F COAGULATION PROCESSES IN TURBULENT COAGULATION
REGIME 343
IMAGE 9
CONTENTS X V
16.7 CONCLUSION 345
16.8 APPENDIX. DERIVATION O F THE COAGULATION COEFFICIENT 346
17 STOKES FLOWS UNDER RANDOM BOUNDARY VELOCITY EXCITATIONS 349
17.1 INTRODUCTION 349
17.2 EXTERIOR STOKES PROBLEM 352
17.2.1 POISSON FORMULA IN POLAR COORDINATES 353
17.3 K-L EXPANSION OF VELOCITY 356
17.3.1 WHITE NOISE EXCITATIONS 356
17.3.2 GENERAL CASE O F HOMOGENEOUS EXCITATIONS 361
17.4 CORRELATION FUNCTION OF THE PRESSURE 366
17.4.1 WHITE NOISE EXCITATIONS 366
17.4.2 HOMOGENEOUS RANDOM BOUNDARY EXCITATIONS 368
17.4.3 VORTICITY AND STRESS TENSOR 368
17.5 INTERIOR STOKES PROBLEM 372
17.6 NUMERICAL RESULTS 374
BIBLIOGRAPHY 381
INDEX 397
|
| any_adam_object | 1 |
| author | Sabel'fel'd, Karl K. 1953- |
| author_GND | (DE-588)121181529 |
| author_facet | Sabel'fel'd, Karl K. 1953- |
| author_role | aut |
| author_sort | Sabel'fel'd, Karl K. 1953- |
| author_variant | k k s kk kks |
| building | Verbundindex |
| bvnumber | BV040977554 |
| classification_rvk | RB 10115 UF 4300 |
| ctrlnum | (OCoLC)830876668 (DE-599)DNB1024907201 |
| dewey-full | 530.15922 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15922 |
| dewey-search | 530.15922 |
| dewey-sort | 3530.15922 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik Geographie |
| format | Book |
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| id | DE-604.BV040977554 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:28:32Z |
| institution | BVB |
| isbn | 9783110296648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025955619 |
| oclc_num | 830876668 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XV, 399 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | de Gruyter |
| record_format | marc |
| spellingShingle | Sabel'fel'd, Karl K. 1953- Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media Lagrange-Formalismus (DE-588)4316154-6 gnd Turbulente Strömung (DE-588)4117265-6 gnd Zufälliges Feld (DE-588)4191094-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Poröser Stoff (DE-588)4046811-2 gnd |
| subject_GND | (DE-588)4316154-6 (DE-588)4117265-6 (DE-588)4191094-1 (DE-588)4057633-4 (DE-588)4046811-2 |
| title | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media |
| title_auth | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media |
| title_exact_search | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media |
| title_full | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media Karl K. Sabelfeld |
| title_fullStr | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media Karl K. Sabelfeld |
| title_full_unstemmed | Random fields and stochastic Lagrangian models analysis and applications in turbulence and porous media Karl K. Sabelfeld |
| title_short | Random fields and stochastic Lagrangian models |
| title_sort | random fields and stochastic lagrangian models analysis and applications in turbulence and porous media |
| title_sub | analysis and applications in turbulence and porous media |
| topic | Lagrange-Formalismus (DE-588)4316154-6 gnd Turbulente Strömung (DE-588)4117265-6 gnd Zufälliges Feld (DE-588)4191094-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Poröser Stoff (DE-588)4046811-2 gnd |
| topic_facet | Lagrange-Formalismus Turbulente Strömung Zufälliges Feld Stochastisches Modell Poröser Stoff |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4097380&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=025955619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sabelfeldkarlk randomfieldsandstochasticlagrangianmodelsanalysisandapplicationsinturbulenceandporousmedia |