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Wolf-Gladrow D.A. — Lattice-gas cellular automata and lattice Boltzmann models
Wolf-Gladrow D.A. — Lattice-gas cellular automata and lattice Boltzmann models



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Название: Lattice-gas cellular automata and lattice Boltzmann models

Автор: Wolf-Gladrow D.A.

Аннотация:

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers.
Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.


Язык: en

Рубрика: Физика/Термодинамика, статистическая физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 274

Добавлена в каталог: 09.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
additive rule      19
Ansatz method      205
Automata rule with memory      20
Automata rule without memory      20
Automata rule, additive      19
Automata rule, legal      20
Automata rule, peripheral      20
Automata rule, symmetric      20
Automata rule, totalistic      20
BBGKY      139
BGK approximation      144 145 165 195 205
Binary digit      153
Bit      153
Bit-function      44
Bit-operator      44
Bit-state      57
bitwise      44
Blood flow      243
Boltzmann approximation      138
Boltzmann distribution      141
Bottom friction      230
Bounce-back rule      80
Boundary condition, complete bounceback      189
Boundary condition, half-way bounceback      190
boundary conditions      79
Boundary, link boundary      189
Boundary, node boundary      189
Breaking of Galilean invariance      73
Burgers equation      138 243
Burnett equations      146
C (programming language)      44
cell      264
Cellular automata      9 15
Cellular automata, elementary      19
Chaining      47
Chapman — Enskog expansion      71
Chapman — Kolmogorov equation      64
Chessboard      40
Chessboard instability      40
Chiral      53
Coarse graining      10
Collision      37 40 57
Collision cross section      140
Collision frequency      144
Collision integral      140
Collision invariants      140
Collision parameter      182
COLOR      137
Complementation      248
Configuration      18
Configuration, global      16
Configuration, local      16
Conservation laws      21
Continuity equation      7
Coriolis parameter      220
Crystal growth      244
Curvilinear coordinates      243
D1Q4      136
D2Q129      134
D2Q13-FHP      101 205
D2Q13-WB      97
D2Q15      98 197
D2Q19      101 129
D2Q21      98 134
D2Q24      95
D2Q25      134
D2Q4      92
D2Q57      134
D2Q7      94
D2Q9      96 131 133 168
Detailed balance      58
Diagonal pair interaction      124
Diffusion equation      21 136 236
Diffusion equation, nonlinear      240 242
Divergence of transport coefficients in 2D      137
DkQb      92
Droplets      244
Dual solids      105
Duality      249
Dynamic similarity      9
Dynamical geometry      137 243
Eddy viscosity coefficient      220
EDGE      264
Ekman number      229
Electrodynamics      17 244
Elementary cellular automata      19 23
Energy conservation      128—130
energy equation      205
Ensemble      64 65
entropy      22
Entropy, maximum entropy principle      156
Entropy, relative      171
Entropy, Renyi      158
Entropy, Shannon      22 156
Euler equation      74 121 177
Evolution operator      40 55
Exclusion principle      40 53 113
Face      112 264
FCHC      10 66 68 95 109 113 118 129 134 265
Fermi — Dirac      40 53 66 74 115
fermions      40
FHP      94 115 129 242
FHP-I      54
FHP-II      54
FHP-III      54
Finite differences      10 232 245
Finite elements      10
Finite volumes      10
Flow in dynamical geometry      137 243
FORTRAN      44
Fractal obstacles      243
Friction coefficient      220
Functional derivative      157
g-factor      73 78
Galilean invariance      90 169
Galilei transformation      73 78
Garden of Eden      22
Generalized lattice tensors      95 128
Gibbs      121
Gibbs' ensemble      64
Glacier flow      243
Global configuration      16
Greek indices      49 57
Grid Reynolds number      227
H-Theorem      244
Head-on collision      40 43
Henon constraints      113 115
Henon's random rule for FCHC      134
HPP      17 39 66 68 92 115 242
Hypercube      108
Identity operator      40
Integer lattice gases      138
Internal energy      205
Intersection      248
Invariants, non-local      57
Invariants, spurious      54
Invariants, staggered      54
Invariants, Zanetti      54 57
Irreversible      22
Ising model      37
Isometric collision rules      113 115
Isometric group      57 113
Isotropic tensors      90 104
Isotropy      10
Jacobi operator      220
Karman vortex street      70 85 123
Kepler      108
Knudsen layer      80
Knudsen number      71 146 148 161
Korteweg — de Vries equation      244
Label      148 149
Lack of information      156
Lagrange multiplier      68 134 156 250
Laplacian friction      220
Laplacian principle of the insufficient reason      155
Large eddy simulation      243
Latin indices      49 57
Lattice gases      37
Lattice symmetry      10
Lattice tensors      40 90 91 128
Lattice tensors, generalized      95
Lattice vectors      39 53
Lattice velocities      39 53
LBGK      160
Legal rule      20 24
Levy-Civita symbol      90
Life      17 31 35
Liouville equation      64 139
Liouville's theorem      22
Local configuration      16
Local Maxwellian      144
Local rule      16
Look-up table      51 114 115 134
Mach number      68 180
Magnetohydrodynamics      137 243
Markov process      16
Mass fraction parameter      208
Maximally discretized molecular dynamics      12
Maxwell distribution      141 143
Maxwell — Boltzmann distribution      141
Maxwell's equations      244
Memory      20; see “Automata rule with memory”
Message      153
Model equations      144
Molecular chaos      140
Molecular Dynamics      11
Momentum advection tensor      72
Moore neighborhood      29
Multi-scale analysis      70 174
Multi-speed FHP      101 205
Multi-speed LGCA      128
Multi-speed models      95 128 195
Multi-spin coding      44
Multiphase flows      137 243
Munk scale      221
Navier — Stokes equation      7 74 145 152 174 177
Neighborhood, Moore      29
Neighborhood, von Neumann      29
Node      39
Nodes, boundary nodes      189
Nodes, dry, wall nodes      190
Nodes, wet, interior, fluid nodes      190
Noise      163
Nondeterministic rules      54
Normal distribution      154
Normalization      57
Normalized momenta      114
Numerical distribution functions      134
Numerical instability      11
Observable      65
Occupation number      48
One-dimensional cellular automata      18
Pair interaction (PI)      118 129 130
PARADISE      22; see “Garden of Eden”
Partial differential equation      21
Pauli principle      40
Penrose lattice      15
Phase space      64
PI      115 118 129 130
Platonic solids      105
Poiseuille flow      190
Poisson equation      137
Polyeder theorem      112
Polygon      264
Polyhedron      264
Polytope      264
Polytope, regular      264
Porous media      137 243
Pressure depends explicitly on velocity      128 159
Pressure-corrected LBM      204
Principle of duality      249
Propagation      37 40 57
Pseudo-random choice      54
Quantum cellular automata      36
quantum mechanics      138 244
Quiescent configuration      20
Random generator      39 50
Random rule      115
Rayleigh — Benard convection      244
Rayleigh — Taylor instability      244
Reaction-diffusion equations      138 242
Reduced densities      139
Reference system      90
Relativistic flows      138
Relaxation toward equilibrium      50 69 83
Renyi entropy      158
Rescaling of time      74
Residue class      18
Rest mass parameters      214
Reversible      22 37 121
Reynolds coefficient      75 117
Reynolds number      8 85 229
Reynolds number, grid      227
Rossby number      227
Rule      18; see “Automata rule”
Rule number      19
Rule, local      16
Schlafli symbol      109 264
Schlafli's criterion      265
Self-dual      105
Semi-detailed balance      58 67 87 113 115 138
Shannon entropy      22; see “Entropy”
Sharp distribution      154
Similarity, law of dynamic      9
simplex      108
Site      39
Sound speed      73
Sound waves      83
Spectral methods      10
Specular reflection      80
Spurious invariants      10 36 41 54 135
Staggered invariants      54 135
Statistical mechanics      36
Stream function      220
Streaming      37 40 57
Stueckelberg condition      58
Sub-lattice      40 118
Supersonic flows      134
Symmetric rule      20
Symmetry      245
Symmetry group      90 91 105
Thermal LBM      205
Thermal LGCA      128
Totalistic rule      20 22—26
Trace      157
traffic flow      36
Transition matrix      58
Transition probability      57
Transsonic flows      134
Turbulence      145 183 243
Turing machine      16 30
union      248
Universality Theorem      54
Universe as a cellular automata      17
Update rule      18; see “Automata rule”
Von Karman vortex street      70 85 123
von Neumann neighborhood      29
Vorticity      76 87
Vorticity equation      183 220 230
Wave propagation      244
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