Lattice gas cellular automata and lattice Boltzmann models: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Schriftenreihe: | Lecture notes in mathematics
1725 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 308 S. graph. Darst. |
| ISBN: | 3540669736 |
Internformat
MARC
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| 100 | 1 | |a Wolf-Gladrow, Dieter |d 1953- |e Verfasser |0 (DE-588)121622312 |4 aut | |
| 245 | 1 | 0 | |a Lattice gas cellular automata and lattice Boltzmann models |b an introduction |c Dieter A. Wolf-Gladrow |
| 246 | 1 | 3 | |a Lattice-gas cellular automata and lattice Boltzmann models |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a IX, 308 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1725 | |
| 650 | 4 | |a Nichtlineare partielle Differentialgleichung - Numerisches Verfahren - Gittermodell - Zellularer Automat | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Cellular automata | |
| 650 | 4 | |a Lattice gas |x Mathematical models | |
| 650 | 4 | |a Maxwell-Boltzmann distribution law | |
| 650 | 0 | 7 | |a Boltzmann-Gleichung |0 (DE-588)4146261-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text | Table of Contents
1. Introduction 1
1.1 Preface 2
1.2 Overview 4
1.3 The basic idea of lattice gas cellular automata and lattice
Boltzmann models 7
1.3.1 The Navier Stokes equation 7
1.3.2 The basic idea 9
1.3.3 Top down versus bottom up 11
1.3.4 LGCA versus molecular dynamics 11
2. Cellular Automata 15
2.1 What are cellular automata? 15
2.2 A short history of cellular automata 16
2.3 One dimensional cellular automata 17
2.3.1 Qualitative characterization of one dimensional cellu¬
lar automata 23
2.4 Two dimensional cellular automata 29
2.4.1 Neighborhoods in 2D 29
2.4.2 Fredkin s game 30
2.4.3 Life 31
2.4.4 CA: what else? Further reading 35
2.4.5 From CA to LGCA 36
VI Table of Contents
3. Lattice gas cellular automata 39
3.1 The HPP lattice gas cellular automata 39
3.1.1 Model description 39
3.1.2 Implementation of the HPP model: How to code
lattice gas cellular automata? 44
3.1.3 Initialization 48
3.1.4 Coarse graining 50
3.2 The FHP lattice gas cellular automata 53
3.2.1 The lattice and the collision rules 53
3.2.2 Microdynamics of the FHP model 59
3.2.3 The Liouville equation 64
3.2.4 Mass and momentum density 65
3.2.5 Equilibrium mean occupation numbers 66
3.2.6 Derivation of the macroscopic equations: multi scale
analysis 69
3.2.7 Boundary conditions 79
3.2.8 Inclusion of body forces 80
3.2.9 Numerical experiments with FHP 83
3.2.10 The 8 bit FHP model 87
3.3 Lattice tensors and isotropy in the macroscopic limit 90
3.3.1 Isotropic tensors 90
3.3.2 Lattice tensors: single speed models 91
3.3.3 Generalized lattice tensors for multi speed models .... 95
3.3.4 Thermal LBMs: D2Q13 FHP (multi speed FHP model) 101
3.3.5 Exercises 104
3.4 Desperately seeking a lattice for simulations in three dimen¬
sions 105
3.4.1 Three dimensions 105
3.4.2 Five and higher dimensions 108
3.4.3 Four dimensions 109
3.5 FCHC 113
3.5.1 Isometric collision rules for FCHC by Henon 113
3.5.2 FCHC, computers and modified collision rules 114
3.5.3 Isometric rules for HPP and FHP 115
Table of Contents VII
3.5.4 What else? 116
3.6 The pair interaction (PI) lattice gas cellular automata 118
3.6.1 Lattice, cells, and interaction in 2D 118
3.6.2 Macroscopic equations 121
3.6.3 Comparison of PI with FHP and FCHC 124
3.6.4 The collision operator and propagation in C and FOR¬
TRAN 124
3.7 Multi speed and thermal lattice gas cellular automata 128
3.7.1 The D3Q19 model 128
3.7.2 The D2Q9 model 131
3.7.3 The D2Q21 model 134
3.7.4 Transsonic and supersonic flows: D2Q25, D2Q57,
D2Q129 134
3.8 Zanetti ( staggered ) invariants 135
3.8.1 FHP 135
3.8.2 Significance of the Zanetti invariants 135
3.9 Lattice gas cellular automata: What else? 137
4. Some statistical mechanics 139
4.1 The Boltzmann equation 139
4.1.1 Five collision invariants and Maxwell s distribution . . . 140
4.1.2 Boltzmann s H theorem 141
4.1.3 The BGK approximation 143
4.2 Chapman Enskog: From Boltzmann to Navier Stokes 145
4.2.1 The conservation laws 146
4.2.2 The Euler equation 147
4.2.3 Chapman Enskog expansion 147
4.3 The maximum entropy principle 153
5. Lattice Boltzmann Models 159
5.1 From lattice gas cellular automata to lattice Boltzmann mod¬
els 159
5.1.1 Lattice Boltzmann equation and Boltzmann equation . 160
5.1.2 Lattice Boltzmann models of the first generation 163
5.2 BGK lattice Boltzmann model in 2D 165
VIII Table of Contents
5.2.1 Derivation of the W, 170
5.2.2 Entropy and equilibrium distributions 171
5.2.3 Derivation of the Navier Stokes equations by multi
scale analysis 174
5.2.4 Storage demand 182
5.2.5 Simulation of two dimensional decaying turbulence .. . 183
5.2.6 Boundary conditions for LBM 189
5.3 Hydrodynamic lattice Boltzmann models in 3D 195
5.3.1 3D LBM with 19 velocities 195
5.3.2 3D LBM with 15 velocities and Koelman distribution . 196
5.3.3 3D LBM with 15 velocities proposed by Chen et al.
(D3Q15) 197
5.4 Equilibrium distributions: the ansatz method 198
5.4.1 Multi scale analysis 199
5.4.2 Negative distribution functions at high speed of sound 203
5.5 Hydrodynamic LBM with energy equation 205
5.6 Stability of lattice Boltzmann models 208
5.6.1 Nonlinear stability analysis of uniform flows 208
5.6.2 The method of linear stability analysis (von Neumann) 210
5.6.3 Linear stability analysis of BGK lattice Boltzmann
models 212
5.6.4 Summary 215
5.7 Simulating ocean circulation with LBM 219
5.7.1 Introduction 219
5.7.2 The model of Munk (1950) 219
5.7.3 The lattice Boltzmann model 222
5.8 A lattice Boltzmann equation for diffusion 232
5.8.1 Finite differences approximation 232
5.8.2 The lattice Boltzmann model for diffusion 233
5.8.3 Multi scale expansion 234
5.8.4 The special case w = 1 236
5.8.5 The general case 236
5.8.6 Numerical experiments 236
5.8.7 Summary and conclusion 237
Table of Contents IX
5.8.8 Diffusion equation with a diffusion coefficient depend¬
ing on concentration 240
5.8.9 Further reading 242
5.9 Lattice Boltzmann model: What else? 243
5.10 Summary and outlook 245
6. Appendix 247
6.1 Boolean algebra 248
6.2 FHP: After some algebra one finds 250
6.3 Coding of the collision operator of FHP II and FHP III in C 254
6.4 Thermal LBM: derivation of the coefficients 258
6.5 Schlafli symbols 264
6.6 Notation, symbols and abbreviations 266
|
| any_adam_object | 1 |
| author | Wolf-Gladrow, Dieter 1953- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV012917117 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:36:00Z |
| institution | BVB |
| isbn | 3540669736 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008793322 |
| oclc_num | 247479906 |
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| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-739 DE-824 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 DE-706 DE-20 |
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| physical | IX, 308 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Wolf-Gladrow, Dieter 1953- Verfasser (DE-588)121622312 aut Lattice gas cellular automata and lattice Boltzmann models an introduction Dieter A. Wolf-Gladrow Lattice-gas cellular automata and lattice Boltzmann models Berlin [u.a.] Springer 2000 IX, 308 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1725 Nichtlineare partielle Differentialgleichung - Numerisches Verfahren - Gittermodell - Zellularer Automat Mathematisches Modell Cellular automata Lattice gas Mathematical models Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Zellularer Automat (DE-588)4190671-8 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zellularer Automat (DE-588)4190671-8 s Strömungsmechanik (DE-588)4077970-1 s Boltzmann-Gleichung (DE-588)4146261-0 s DE-604 Navier-Stokes-Gleichung (DE-588)4041456-5 s Lecture notes in mathematics 1725 (DE-604)BV000676446 1725 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008793322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wolf-Gladrow, Dieter 1953- Lattice gas cellular automata and lattice Boltzmann models an introduction Lecture notes in mathematics Nichtlineare partielle Differentialgleichung - Numerisches Verfahren - Gittermodell - Zellularer Automat Mathematisches Modell Cellular automata Lattice gas Mathematical models Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Zellularer Automat (DE-588)4190671-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4146261-0 (DE-588)4041456-5 (DE-588)4190671-8 (DE-588)4077970-1 (DE-588)4113937-9 |
| title | Lattice gas cellular automata and lattice Boltzmann models an introduction |
| title_alt | Lattice-gas cellular automata and lattice Boltzmann models |
| title_auth | Lattice gas cellular automata and lattice Boltzmann models an introduction |
| title_exact_search | Lattice gas cellular automata and lattice Boltzmann models an introduction |
| title_full | Lattice gas cellular automata and lattice Boltzmann models an introduction Dieter A. Wolf-Gladrow |
| title_fullStr | Lattice gas cellular automata and lattice Boltzmann models an introduction Dieter A. Wolf-Gladrow |
| title_full_unstemmed | Lattice gas cellular automata and lattice Boltzmann models an introduction Dieter A. Wolf-Gladrow |
| title_short | Lattice gas cellular automata and lattice Boltzmann models |
| title_sort | lattice gas cellular automata and lattice boltzmann models an introduction |
| title_sub | an introduction |
| topic | Nichtlineare partielle Differentialgleichung - Numerisches Verfahren - Gittermodell - Zellularer Automat Mathematisches Modell Cellular automata Lattice gas Mathematical models Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Zellularer Automat (DE-588)4190671-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Nichtlineare partielle Differentialgleichung - Numerisches Verfahren - Gittermodell - Zellularer Automat Mathematisches Modell Cellular automata Lattice gas Mathematical models Maxwell-Boltzmann distribution law Boltzmann-Gleichung Navier-Stokes-Gleichung Zellularer Automat Strömungsmechanik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008793322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT wolfgladrowdieter latticegascellularautomataandlatticeboltzmannmodelsanintroduction AT wolfgladrowdieter latticegascellularautomataandlatticeboltzmannmodels |