Approximate deconvolution models of turbulence: analysis, phenomenology and numerical analysis
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Lecture notes in mathematics
2042 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3873356&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=024541416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VIII, 184 S. Ill., graph. Darst. |
| ISBN: | 3642244084 9783642244087 |
Internformat
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| 245 | 1 | 0 | |a Approximate deconvolution models of turbulence |b analysis, phenomenology and numerical analysis |c William J. Layton ; Leo G. Rebholz |
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| 300 | |a VIII, 184 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-2042 |
|---|---|
| DE-BY-TUM_katkey | 1823164 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071482452 |
| _version_ | 1821934990452064258 |
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 THE NAVIER-STOKES EQUATIONS 3
1.1.1 INTEGRAL INVARIANTS 5
1.1.2 THE K41 THEORY OF HOMOGENEOUS, ISOTROPIE TURBULENCE 7
1.2 LARGE EDDY SIMULATION 13
1.3 EDDY VISCOSITY CLOSURES 14
1.4 CLOSURE BY VAN CITTERT APPROXIMATE DECONVOLUTION 17 1.4.1 THE
BARDINA MODEL 20
1.4.2 THE ACCURACY OF VAN CITTERT DECONVOLUTION 21
1.5 APPROXIMATE DECONVOLUTION REGULARIZATIONS 25
1.5.1 TIME RELAXATION 25
1.5.2 THE LERAY-DECONVOLUTION REGULARIZATION 27
1.5.3 THE NS-ALPHA REGULARIZATION 28
1.5.4 THE NS-OMEGA REGULARIZATION 28
1.6 THE PROBLEM OF BOUNDARY CONDITIONS 29
1.6.1 THE COMMUTATOR ERROR 30
1.6.2 NEAR WALL MODELING 30
1.6.3 CHANGING THE AVERAGING OPERATOR TO A DIFFERENTIAL FILTER 31
1.6.4 AD HOC CORRECTIONS AND REGULARIZATION MODELS 32 1.6.5 NEAR WALL
RESOLUTION 32
1.7 TEN OPEN PROBLEMS IN THE ANALYSIS OF ADMS 32
2 LARGE EDDY SIMULATION 35
2.1 THE IDEA OF LARGE EDDY SIMULATION 35
2.1.1 DIFFERING DYNAMICS OF THE LARGE AND SMALL EDDIES ... 35 2.1.2 THE
EDDY-VISCOSITY HYPOTHESIS/BOUSSINESQ ASSUMPTION 36
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1014764211
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.2 LOCAL SPACIAL AVERAGES 37
2.2.1 TOP HAT FILTER 39
2.2.2 DISCRETE FILTERS 40
2.2.3 WEIGHTED DISCRETE FILTERS 40
2.2.4 OTHER FILTERS 41
2.2.5 WEIGHTED COMPACT DISCRETE FILTER FROM [SAKOLA].... 41 2.2.6
DIFFERENTIAL FILTERS 42
2.2.7 SCALE SPACE: WHAT IS THE RIGHT AVERAGING? 45
2.3 THESFNSE 46
2.4 EDDY VISCOSITY MODELS 48
2.4.1 A FIRST CHOICE OF V T 50
2.5 THE SMAGORINSKY MODEL 51
2.6 SOME SMAGORINSKY VARIANTS 54
2.6.1 USING THE Q-CRITERION 55
2.6.2 A MULTISCALE TURBULENT DIFFUSION COEFFICIENT 56 2.6.3 LOCALIZATION
OF EDDY VISCOSITY IN SCALE SPACE 56 2.6.4 VREMAN S EDDY VISCOSITY 57
2.7 A GLIMPSE INTO NEAR WALL MODELS 58
2.8 REMARKS 59
APPROXIMATE DECONVOLUTION OPERATORS AND MODELS 61 3.1 USEFUL
DECONVOLUTION OPERATORS 61
3.1.1 APPROXIMATE DECONVOLUTION 63
3.2 LES APPROXIMATE DECONVOLUTION MODELS 65
3.3 EXAMPLES OF APPROXIMATE DECONVOLUTION OPERATORS 66 3.3.1 TIKHONOV
REGULARIZATION 67
3.3.2 TIKHONOV-LAVRENTIEV REGULARIZATION 67
3.3.3 A VARIANT ON TIKHONOV-LAVRENTIEV REGULARIZATION 68 3.3.4 THE VAN
CITTERT REGULARIZATION 68
3.3.5 VAN CITTERT WITH RELAXATION PARAMETERS 68
3.3.6 OTHER APPROXIMATE DECONVOLUTION METHODS 69 3.4 ANALYSIS OF VAN
CITTERT DECONVOLUTION 70
3.4.1 PROOF 75
3.5 DISCRETE DIFFERENTIAL FILTERS 75
3.6 REVERSIBILITY OF APPROXIMATE DECONVOLUTION MODELS 78 3.7 THE ZEROTH
ORDER MODEL 78
3.7.1 PROOF 81
3.8 REMARKS 87
PHENOMENOLOGY OF A D MS 89
4.1 BASIC PROPERTIES OF ADMS 89
4.2 THE ADM ENERGY CASCADE 91
4.2.1 ANOTHER APPROACH TO THE ADM ENERGY SPECTRUM 94 4.2.2 THE ADM
HELICITY CASCADE 95
IMAGE 3
CONTENTS
4.3 THE ADM MICRO-SCALE 95
4.3.1 DESIGN OF AN EXPERIMENTAL TEST OF THE MODEL S ENERGY CASCADE 97
4.4 REMARKS 97
TIME RELAXATION TRUNCATES SCALES 99
5.1 TIME RELAXATION 99
5.2 THE MICROSCALE OF LINEAR TIME RELAXATION 102
5.2.1 CASE 1: FULLY RESOLVED 109
5.2.2 CASE 2: UNDER RESOLVED 109
5.2.3 CASE 3: PERFECT RESOLUTION 110
5.3 TIME RELAXATION DOES NOT ALTER SHOCK SPEEDS 110
5.4 NONLINEAR TIME RELAXATION 112
5.4.1 OPEN QUESTION 1: DOES NONLINEAR TIME RELAXATION DISSIPATE ENERGY
IN ALL CASES? 113 5.4.2 OPEN QUESTION 2: IF NOT, WHAT IS THE SIMPLEST
MODIFICATION TO NONLINEAR TIME
RELAXATION THAT ALWAYS DISSIPATES ENERGY? 113 5.4.3 OPEN QUESTION 3: HOW
IS NONLINEAR TIME RELAXATION TO BE DISCRETIZED IN TIME SO AS
TO BE UNCONDITIONALLY STABLE AND REQUIRE FILTERING ONLY OF KNOWN
FUNCTIONS? 113
5.5 ANALYSIS OF A NONLINEAR TIME RELAXATION 114
5.5.1 OPEN QUESTION 4: IS THE EXTRA (I - G) NECESSARY TO ENSURE ENERGY
DISSIPATION OR JUST A MATHEMATICAL CONVENIENCE? 115
5.5.2 OPEN QUESTION 5: IF THE EXTRA (I - G) IS NECESSARY, HOW IS IT TO
BE DISCRETIZED IN TIME? ... 115 5.5.3 THEN = 0CASE 117
5.5.4 THE ANALYSIS OF LILLY 118
5.5.5 OPEN QUESTION 8: IS IT POSSIBLE TO EXTEND THE ABOVE CALCULATION OF
THE OPTIMAL RELAXATION PARAMETER TO THE ORIGINAL VERSION OF NONLINEAR
TIME RELAXATION? 120 5.6 REMARKS 120
THE LERAY-DECONVOLUTION REGULARIZATION 121
6.1 THE LERAY REGULARIZATION 121
6.2 DUNCA S LERAY-DECONVOLUTION REGULARIZATION 124
6.3 ANALYSIS OF THE LERAY-DECONVOLUTION REGULARIZATION 125 6.3.1
EXISTENCE OF SOLUTIONS 125
6.3.2 PROOF 126
6.3.3 LIMITS OF THE LERAY-DECONVOLUTION REGULARIZATION 129 6.4 ACCURACY
OF THE LERAY-DECONVOLUTION FAMILY 130
6.4.1 THE CASE OF HOMOGENEOUS, ISOTROPIE TURBULENCE 131
IMAGE 4
VIII CONTENTS
6.5 MICROSCALES 134
6.5.1 CASE 1 135
6.5.2 CASE 2 136
6.6 DISCRETIZATION 136
6.7 NUMERICAL EXPERIMENTS WITH LERAY-DECONVOLUTION 138 6.7.1 CONVERGENCE
RATE VERIFICATION 138
6.7.2 TWO-DIMENSIONAL CHANNEL FLOW OVER A STEP 139
6.7.3 THREE-DIMENSIONAL CHANNEL FLOW OVER A STEP 142 6.8 REMARKS 144
7 NS-ALPHA- AND NS-OMEGA-DECONVOLUTION REGULARIZATIONS 145 7.1 INTEGRAL
INVARIANTS OF THE NSE 145
7.2 THE NS-ALPHA REGULARIZATION 147
7.2.1 THE PERIODIC CASE 147
7.2.2 DISCRETIZATIONS OF THE NS-ALPHA REGULARIZATION 150 7.3 THE
NS-OMEGA REGULARIZATION 151
7.3.1 MOTIVATION FOR NS-W: THE CHALLENGES OF TIME DISCRETIZATION 153
7.4 COMPUTATIONAL PROBLEMS WITH ROTATION FORM 154
7.5 NUMERICAL EXPERIMENTS WITH NS-A 157
7.5.1 TWO-DIMENSIONAL FLOW OVER A STEP 157
7.5.2 THREE-DIMENSIONAL FLOW OVER A STEP 157
7.6 MODEL SYNTHESIS 158
7.6.1 SYNTHESIS OF NS-A AND W MODELS 159
7.6.2 SCALE TRUNCATION, EDDY VISCOSITY, VMMS AND TIME RELAXATION 160
7.7 REMARKS 161
A DECONVOLUTION UNDER THE NO-SLIP CONDITION AND THE LOSS OF REGULARITY
163
A. 1 REGULARITY BY DIRECT ESTIMATION OF DERIVATIVES 164
A.2 THE BOOTSTRAP ARGUMENT 167
A.2.1 THECASEFC = 3 167
A.2.2 OBSERVATION 167
A.3 EXAMPLES 170
A.4 APPLICATION TO DIFFERENTIAL FILTERS 172
A.5 REMARKS 173
REFERENCES 175
INDEX 183
|
| any_adam_object | 1 |
| author | Layton, William J. Rebholz, Leo G. |
| author_GND | (DE-588)1020165960 (DE-588)1020166274 |
| author_facet | Layton, William J. Rebholz, Leo G. |
| author_role | aut aut |
| author_sort | Layton, William J. |
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| building | Verbundindex |
| bvnumber | BV039692687 |
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| classification_tum | PHY 223f MAT 650f |
| ctrlnum | (OCoLC)767771698 (DE-599)DNB1014764211 |
| dewey-full | 532.0527 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics 515 - Analysis |
| dewey-raw | 532.0527 515.353 |
| dewey-search | 532.0527 515.353 |
| dewey-sort | 3532.0527 |
| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV039692687 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:00:13Z |
| institution | BVB |
| isbn | 3642244084 9783642244087 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024541416 |
| oclc_num | 767771698 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-11 DE-83 DE-188 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-11 DE-83 DE-188 |
| physical | VIII, 184 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Layton, William J. Rebholz, Leo G. Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis Lecture notes in mathematics Approximation (DE-588)4002498-2 gnd Turbulente Strömung (DE-588)4117265-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4117265-6 (DE-588)4114528-8 (DE-588)4125161-1 |
| title | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis |
| title_auth | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis |
| title_exact_search | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis |
| title_full | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis William J. Layton ; Leo G. Rebholz |
| title_fullStr | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis William J. Layton ; Leo G. Rebholz |
| title_full_unstemmed | Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis William J. Layton ; Leo G. Rebholz |
| title_short | Approximate deconvolution models of turbulence |
| title_sort | approximate deconvolution models of turbulence analysis phenomenology and numerical analysis |
| title_sub | analysis, phenomenology and numerical analysis |
| topic | Approximation (DE-588)4002498-2 gnd Turbulente Strömung (DE-588)4117265-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Approximation Turbulente Strömung Mathematisches Modell Inverses Problem |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3873356&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=024541416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT laytonwilliamj approximatedeconvolutionmodelsofturbulenceanalysisphenomenologyandnumericalanalysis AT rebholzleog approximatedeconvolutionmodelsofturbulenceanalysisphenomenologyandnumericalanalysis |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-2042 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |