Chapter
Chapter 2 Microdynamics: general formalism
2.1 Basic concepts and notation
2.1.1 The lattice and the velocity vectors
2.1.4 Generalized observables
2.2 The microdynamic equation
2.2.2 The propagation operator
2.2.3 The collision operator
2.2.4 Analytic expressions of the microdynamic equation
2.3 Microscopic properties of a lattice gas
2.3.1 Detailed and semi-detailed balance
2.3.5 Crystallographic isotropy
2.4.1 Solid impermeable obstacles
2.4.2 Sources and sinks of observable quantities
Chapter 3 Microdynamics: various examples
3.1.1 The micro dynamical equation
3.1.2 Microscopic properties
3.2.1 The micro dynamical equation
3.2.2 Microscopic properties
3.3.1 The microdynamical equation
3.3.2 Microscopic properties
3.4.1 The microdynamical equation
3.4.2 Microscopic properties
3.5 The 'colored' FHP model (CFHP)
3.5.1 The microdynamical equation
3.5.2 Microscopic properties
3.6.1 The microdynamical equation
3.6.2 Microscopic properties
3.7 Three-dimensional models
3.7.1 Models with multiple links
3.7.2 Models with biased collisions
3.7.5 The microdynamical equation
3.7.6 Microscopic properties
Chapter 4 Equilibrium statistical mechanics
4.1 The Liouville description
4.1.3 The lattice Liouville equation
4.2 The Boltzmann description
4.2.1 The Boltzmann approximation
4.2.2 The lattice Boltzmann equation
4.3.1 Some basics about communication and information
4.3.2 The H-theorem for lattice gases
4.4 Global equilibrium macrostates
4.4.1 The Liouville approach
4.4.2 The lattice Boltzmann approach
4.4.3 The variational approach
4.5 Natural parameterization of equilibria
4.5.1 Low-speed equilibria for single-species non-thermal models
4.5.2 Nearly equally distributed equilibria for thermal models
4.6 Statistical thermodynamics
4.7 Static correlation functions
Chapter 5 Macrodynamics: Chapman-Enskog method
5.1 Local equilibria and the hydrodynamic limit
5.2 The multi-scale expansion for macrodynamics
5.2.1 The scale separation parameter
5.2.2 Perturbed local equilibrium
5.2.3 Macroscopic space and time scales
5.2.4 The averaged microdynamic equation
5.2.5 The expansion in powers of e
5.3 First order macrodynamics
5.3.1 Solvability conditions for the first order problem
5.3.2 Solution of the first order problem
5.4 Second order macrodynamics
5.4.1 Solvability conditions for the second order problem
5.5 The macrodynamic equations
5.6 Transport coefficients within the Boltzmann approximation
5.7.1 First order macrodynamics
5.7.2 Second order macrodynamics
5.7.3 The macrodynamic equation
5.7.4 The transport coefficients
Chapter 6 Linearized hydrodynamics
6.1 The linearized Boltzmann equation
6.2 Slow and fast variables
6.3 The hydrodynamic limit
6.3.1 The coupling function
6.3.2 The memory function
6.3.3 The random force term
6.3.4 The long-wavelength, long-time limit
Chapter 7 Hydrodynamic fluctuations
7.1 The dynamic structure factor
7.2 Fluctuation correlations
7.3 The hydrodynamic modes
7.3.1 The spectral decomposition
7.4 The hydrodynamic spectrum
7.5 The eigenvalue spectrum
7.5.1 Hydrodynamic regime: klf << 1
7.5.2 Generalized hydrodynamic regime: klf < 1
7.5.3 Kinetic regime: klf >, 1
7.7 Diffusion and correlations
7.7.1 The two-species lattice gas
7.7.2 The hydrodynamic limit
Chapter 8 Macrodynamics: projectors approach
8.2 Multiple scales analysis
8.3 The hydrodynamic equations
8.4 Linear response and Green-Kubo coefficients
Chapter 9 Hydrodynamic regimes
9.2 The incompressible limit
9.3.2 Four-dimensional models
9.3.3 Lattice gases to simulate real fluid dynamics
Chapter 10 Lattice gas simulations
10.1 Lattice gas algorithms on dedicated machines
10.2 Lattice gas algorithms on general purpose computers
10.2.1 Channel-wise vs. node-wise storage
10.2.2 Collision strategies
10.3 Essential features of a lattice gas simulation code
10.3.2 Raw physical data extraction
10.4 Measurement of basic lattice gas properties
10.4.1 Measuring g(p) and v(p)
10.4.2 Measuring cs(p) and v'(p)
10.4.3 An example: the FCHC-3 model
10.5 Examples of lattice gas simulations
10.5.1 The Kelvin-Helmholtz instability
10.5.2 Particle aggregation
10.5.3 Two-dimensional flow past an obstacle
10.5.4 Three-dimensional flow past an obstacle
10.5.5 Two-dimensional flow of a two-phase fluid in a porous medium
Chapter 11 Guide for further reading
11.1 The historical 'roots'
11.1.1 Discrete kinetic theory
11.2 Three-dimensional models
11.3 Theoretical analyses
11.3.1 General lattice gas theory
11.3.2 Statistical physics and thermodynamics
11.3.3 Violation of semi-detailed balance
11.3.4 Invariants and conservation laws
11.3.5 Obstacles and Knudsen layers
11.4 Models with particular features
11.4.1 Fluid mixtures and colloids
11.4.2 Reaction-diffusion systems
11.4.3 Immiscible fluids and free interfaces
11.4.4 Flow in porous media
11.4.5 Thermo-hydrodynamics
11.5 Lattice Boltzmann method
11.6 Lattice Bhatnagar-Gross-Krook model
11.7 Numerical simulations and implementations
11.7.1 Implementation on dedicated hardware
11.7.2 Simulations on general purpose computers
11.8 Books and review articles
Appendix Mathematical details
Lattice Gas Hydrodynamics
( Cambridge Nonlinear Science Series )
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