Non-reflecting boundary conditions for the Lattice Boltzmann method:
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| Format: | Thesis Book |
| Language: | English |
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2013
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| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130528-1129700-0-6 Inhaltsverzeichnis |
| Physical Description: | X, 204 S. graph. Darst. |
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| adam_text | TECHNISCHE UNIVERSITAT MUNCHEN
LEHRSTUHL FIIR COMPUTATION IN ENGINEERING
NON-REFLECTING BOUNDARY CONDITIONS
FOR THE LATTICE BOLTZMANN METHOD
MARTIN B. SCHLAFFER
VOLLSTANDIGER ABDRUCK DER VON DER INGENIEURFAKULTAT BAU GEO UMWELT DER
TECHNISCHEN UNIVERSITAT MUNCHEN ZUR ERLANGUNG DES AKADEMISCHEN GRADES
EINES
DOKTOR-INGENIEURS
GENEHMIGTEN DISSERTATION.
VORSITZENDER: UNIV.-PROF. DR.-ING. HABIL. MICHAEL MANHART
PRIIFER DER DISSERTATION:
1. UNIV.-PROF. DR.RER.NAT. ERNST RANK
2. UNIV.-PROF. DR.-ING. HABIL. MANFRED KRAFCZYK
TECHNISCHE UNIVERSITAT BRAUNSCHWEIG
3. UNIV.-PROF. DR.-ING. HABIL. GERHARD H. MIILLER
DIE DISSERTATION WURDE AM 06.02.2013 BEI DER TECHNISCHEN UNIVERSITAT
MUNCHEN EINGEREICHT
UND DURCH DIE INGENIEURFAKULTAT BAU GEO UMWELT AM 28.05.2013 ANGENOMMEN.
HTTP://D-NB.INFO/1048189775
V
III
IX
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31
CONTENTS
ACKNOWLEDGMENTS
TABLE OF SYMBOLS
1 INTRODUCTION
2 GOVERNING EQUATIONS IN FLUID MECHANICS
2.1 CONSERVATION PROPERTIES
2.1.1 SCALAR CONSERVATION LAW
2.1.2 VECTOR CONSERVATION LAW
2.2 CONTINUITY EQUATION
2.3 NAVIER-STOKES EQUATION
2.4 ENERGY EQUATION
3 LATTICE BOLTZMANN METHOD
3.1 BOLTZMANN EQUATION
3.1.1 DENSITY DISTRIBUTION FUNCTION
3.1.2 MOMENTS OF THE DENSITY DISTRIBUTION FUNCTION
3.1.3 BOLTZMANN EQUATION
3.1.4 FROM BOLTZMANN EQUATION TO CONTINUITY EQUATION . . .
3.2 SOLUTION OF THE BOLTZMANN EQUATION
3.2.1 GENERAL SOLUTION OF SIMPLIFIED BOLTZMANN EQUATION . . .
3.2.2 EQUILIBRIUM DISTRIBUTION FUNCTION
3.2.3 COLLISION MODELING
3.2.4 NONDIMENSIONALIZATION OF THE BGK BOLTZMANN EQUATION
3.2.5 LATTICE UNIT SET
3.3 LATTICE BOLTZMANN EQUATION
3.4 ANALYSIS OF THE LBGK EQUATION
3.4.1 CHAPMAN-ENSKOG ANALYSIS
3.4.2 MOMENT BASIS
3.5 INCOMPRESSIBLE LBM
3.5.1 SRT
3.5.2 MRT
VI
CONTENTS
4 BOUNDARY CONDITIONS FOR LBM 33
4.1 GENERAL CLASSIFICATION 33
4.2 BOUNCE-BACK BOUNDARY CONDITIONS 34
4.3 ZOU-HE BOUNDARY CONDITIONS 35
4.3.1 ERROR OF THE NON-EQUILIBRIUM BOUNCE-BACK RELATION 37
5 NON-REFLECTING BOUNDARY CONDITIONS 41
5.1 FILTERING METHODS 41
5.1.1 CONTINUOUS LOW-PASS FILTER 42
5.1.2 DISCRETE LOW-PASS FILTER 42
5.1.3 LOW-PASS FILTER BOUNDARY CONDITION FOR LBM 46
5.1.4 ID PRESSURE WAVE TEST CASE 48
5.1.5 DISCUSSION OF ID PRESSURE WAVE TEST CASE 51
5.2 CHARACTERISTIC BASED METHODS 54
5.2.1 PRINCIPLE OF THE LODI METHOD 54
5.2.2 LODI BOUNDARY CONDITIONS FOR LBM IN ID 58
5.2.3 LODI BOUNDARY CONDITIONS FOR LBM IN 2D 62
5.2.4 2D PRESSURE WAVE TEST CASE 65
5.2.5 2D PRESSURE WAVE TEST CASE FOR LODI BCS 69
6 IMPEDANCE BOUNDARY CONDITIONS 81
6.1 IMPEDANCE CONDITION ID 81
6.1.1 IMPEDANCE CONDITION FOR COMPRESSIBLE LBM 82
6.1.2 IMPEDANCE CONDITION FOR INCOMPRESSIBLE LBM 85
6.1.3 ADAPTION RELATIVE TO FIXED REFERENCE LEVEL 85
6.2 IMPEDANCE BOUNDARY CONDITIONS FOR LBM IN ID 87
6.2.1 ADAPTION RELATIVE TO LAST TIME STEP 87
6.2.2 ADAPTION RELATIVE TO FIXED REFERENCE LEVEL 90
6.2.3 HIGHLY VISCOUS FLOW 92
6.3 IMPEDANCE BOUNDARY CONDITIONS FOR LBM IN 2D 94
6.3.1 * ADAPTION IN NORMAL DIRECTION FOR COMPRESSIBLE LBM 94
6.3.2 ADAPTION IN NORMAL DIRECTION, COMPRESSIBLE LBM, FIXED REFERENCE
LEVEL 95
6.3.3 ISOTROPIC ADAPTION FOR COMPRESSIBLE LBM 95
6.3.4 ADAPTION IN NORMAL DIRECTION FOR INCOMPRESSIBLE LBM 98
6.3.5 ADAPTION IN NORMAL DIRECTION, INCOMPRESSIBLE LBM, FIXED REFERENCE
LEVEL 99
6.3.6 ISOTROPIC ADAPTION FOR INCOMPRESSIBLE LBM 99
6.4 2D PRESSURE WAVE TEST CASE FOR IMPEDANCE BCS 101
6.5 COMPENSATION OF NON-EQUILIBRIUM BOUNCE-BACK ERROR 106
7 BOUNDARY STATE ADAPTION FOR IMPEDANCE BOUNDARY CONDITIONS 109
7.1 VELOCITY ADAPTION 110
7.1.1 COMPRESSIBLE LBM 110
7.1.2 INCOMPRESSIBLE LBM ILL
7.2 PRESSURE ADAPTION 112
CONTENTS
VII
7.2.1 COMPRESSIBLE LBM 112
7.2.2 INCOMPRESSIBLE LBM 113
7.3 SOUND PRESSURE LEVEL AS ADAPTION CRITERIA 113
7.4 BENCHMARK: FLOW AROUND CYLINDER 114
7.4.1 RESULTS OF STEADY BENCHMARK 116
7.4.2 RESULTS OF UNSTEADY BENCHMARK 121
8 IMPEDANCE BOUNDARY CONDITIONS FOR LBM SHALLOW WATER MODEL 127
8.1 SHALLOW WATER MODEL FOR THE LBM 127
8.2 IMPEDANCE BOUNDARY CONDITION 129
8.3 SIMULATION AND RESULTS 130
9 CONCLUSION AND OUTLOOK 133
A CODE EXAMPLES 135
A.L LODI BOUNDARY CONDITION, ID 135
A.2 LODI BOUNDARY CONDITION, 2D, COMPRESSIBLE LBM 136
A.3 LODI BOUNDARY CONDITION, 2D, INCOMPRESSIBLE LBM 137
A.4 IMPEDANCE BOUNDARY CONDITION, ID 138
A.5 IMPEDANCE BC, FIXED REFERENCE LEVEL, ID 138
A.6 IMPEDANCE BC, 2D, COMPRESSIBLE, ADAPTION IN NORMAL DIRECTION 139
A.7 IMPEDANCE BC, 2D, COMPRESSIBLE, ADAPTION IN NORMAL DIRECTION, FIXED
REFERENCE LEVEL 140
A.8 IMPEDANCE BC, 2D, COMPRESSIBLE, FULL ADAPTION 141
A.9 IMPEDANCE BC, 2D, COMPRESSIBLE, FULL ADAPTION, FIXED REFERENCE
LEVEL.... 142
A. 10 IMPEDANCE BC, 2D, COMPRESSIBLE, FULL ADAPTION WITH RELAXATION,
RIGHT
HAND SIDE 144
A.11 IMPEDANCE BC, 2D, INCOMPRESSIBLE, ADAPTION IN NORMAL DIRECTION 146
A. 12 IMPEDANCE BC, 2D, INCOMPRESSIBLE, ADAPTION IN NORMAL DIRECTION,
FIXED REFER
ENCE LEVEL 147
A.13 IMPEDANCE BC, 2D, INCOMPRESSIBLE, FULL ADAPTION 148
A.14 IMPEDANCE BC, 2D, INCOMPRESSIBLE, FULL ADAPTION, FIXED REFERENCE
LEVEL . . . 149
A. 15 IMPEDANCE BC, 2D, INCOMPRESSIBLE, FULL ADAPTION WITH RELAXATION,
RIGHT
HAND SIDE 150
A. 16 IMPEDANCE VELOCITY BC, 2D, COMPRESSIBLE 152
A. 17 IMPEDANCE PRESSURE BC, 2D, COMPRESSIBLE 153
A. 18 IMPEDANCE BC FOR NONLINEAR SHALLOW WATER LBM 154
B RESULTS 2D PRESSURE WAVE TEST CASE, IMPEDANCE BCS 155
B.L COMPRESSIBLE LBM, RESTING FLUID 155
B.2 COMPRESSIBLE LBM, PARABOLIC VELOCITY PROFILE 158
B.3 COMPRESSIBLE LBM, FIXED REFERENCE LEVEL, RESTING FLUID 161
B.4 COMPRESSIBLE LBM, FIXED REFERENCE LEVEL, PARABOLIC VELOCITY PROFILE
164
B.5 INCOMPRESSIBLE LBM, RESTING FLUID 166
B.6 INCOMPRESSIBLE LBM, PARABOLIC VELOCITY PROFILE 169
B.7 INCOMPRESSIBLE LBM, FIXED REFERENCE LEVEL, RESTING FLUID 172
VIII CONTENTS
B.8 INCOMPRESSIBLE LBM, FIXED REFERENCE LEVEL, PARABOLIC VELOCITY
PROFILE .... 175
B.9 COMPRESSIBLE LBM, FULL ADAPTION, RESTING FLUID 177
B.10 COMPRESSIBLE LBM, FULL ADAPTION, PARABOLIC VELOCITY PROFILE 180
B.LL COMPRESSIBLE LBM, FULL ADAPTION, FIXED REFERENCE LEVEL, RESTING
FLUID . . . 183
B.12 COMPRESSIBLE LBM, FULL ADAPTION, FIXED REFERENCE LEVEL, PARABOLIC
VELOCITY
PROFILE 186
B.13 INCOMPRESSIBLE LBM, FULL ADAPTION, RESTING FLUID 188
B.14 INCOMPRESSIBLE LBM, FULL ADAPTION, PARABOLIC VELOCITY PROFILE 191
B.15 INCOMPRESSIBLE LBM, FULL ADAPTION, FIXED REFERENCE LEVEL, RESTING
FLUID . . 194
B.16 INCOMPRESSIBLE LBM, FULL ADAPTION, FIXED REFERENCE LEVEL, PARABOLIC
VELOCITY
PROFILE 197
|
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| spelling | Schlaffer, Martin B. Verfasser aut Non-reflecting boundary conditions for the Lattice Boltzmann method Martin B. Schlaffer 2013 X, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Mit einer Zssfassung in dt. Sprache Fluidtechnik (DE-588)4154793-7 gnd rswk-swf Gitter-Boltzmann-Methode (DE-588)4772570-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gitter-Boltzmann-Methode (DE-588)4772570-9 s Fluidtechnik (DE-588)4154793-7 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130528-1129700-0-6 http://mediatum.ub.tum.de/node?id=1129700 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130528-1129700-0-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027059546&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schlaffer, Martin B. Non-reflecting boundary conditions for the Lattice Boltzmann method Fluidtechnik (DE-588)4154793-7 gnd Gitter-Boltzmann-Methode (DE-588)4772570-9 gnd |
| subject_GND | (DE-588)4154793-7 (DE-588)4772570-9 (DE-588)4113937-9 |
| title | Non-reflecting boundary conditions for the Lattice Boltzmann method |
| title_auth | Non-reflecting boundary conditions for the Lattice Boltzmann method |
| title_exact_search | Non-reflecting boundary conditions for the Lattice Boltzmann method |
| title_full | Non-reflecting boundary conditions for the Lattice Boltzmann method Martin B. Schlaffer |
| title_fullStr | Non-reflecting boundary conditions for the Lattice Boltzmann method Martin B. Schlaffer |
| title_full_unstemmed | Non-reflecting boundary conditions for the Lattice Boltzmann method Martin B. Schlaffer |
| title_short | Non-reflecting boundary conditions for the Lattice Boltzmann method |
| title_sort | non reflecting boundary conditions for the lattice boltzmann method |
| topic | Fluidtechnik (DE-588)4154793-7 gnd Gitter-Boltzmann-Methode (DE-588)4772570-9 gnd |
| topic_facet | Fluidtechnik Gitter-Boltzmann-Methode Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1129700 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130528-1129700-0-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027059546&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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