Preface
Acknowledgements
I. Theory
1.
Kinetic theory
1.1.
Atomistic dynamics
1.2.
Relaxation to local equilibrium
1.3.
H
-theorem
1.4.
Length scales and transport phenomena
1.5.
Chapman-Enskog procedure
1.6.
The Navier-Stokes equations
1.7.
Bhatnagar-Gross-Krook model equation
1.8.
Exercises
2.
Lattice gas cellular automata
2.1.
Fluids in Gridland: the Frisch-Hasslacher-Pomeau automaton
2.2.
Fluons in action: LGCA microdynamic evolution
2.3.
From LGCA to Navier-Stokes
2.4.
Practical implementation
2.5.
Lattice gas diseases and how to cure them
2.6.
Summary
2.7.
Exercises
3.
Lattice Boltzmann models with underlying Boolean microdynamics
3.1.
Nonlinear LBE
3.2.
The quasilinear LBE
3.3.
The scattering matrix A(ij)
3.4.
Numerical experiments
3.5.
Exercises
4.
Lattice Boltzmann models without underlying Boolean microdynamics
4.1.
LBE with enhanced collisions
4.2.
Hydrodynamic and ghost fields
4.3.
The route to Navier-Stokes: adiabatic assumption
4.4.
The mirage of zero viscosity
4.5.
Numerical experiments
4.6.
Exercises
5.
Lattice Bhatnagar-Gross-Krook
5.1.
Single-time relaxation
5.2.
LBGK equilibria
5.3.
LBGK versus LBE
5.4.
Relation to continuum kinetic theory
5.5.
Relation to discrete velocity models
5.6.
LBE genealogy
5.7.
Warm-up code
5.8.
Exercises
II. Fluid dynamics applications and advanced theory
6.
Boundary conditions
6.1.
General formulation of LBE boundary conditions
6.2.
Survey of various boundary conditions
6.3.
Open boundaries
6.4.
Complex (misaligned) boundaries
6.5.
Exactly incompressible LBE schemes
6.6.
Exercises
7.
Flows at moderate Reynolds numbers
7.1.
Moderate Reynolds flows in simple geometry
7.2.
LBE implementation
7.3.
Boundary conditions
7.4.
Flows past obstacles
7.5.
More on the pressure field: Poisson-freedom
7.6.
Exercises
8.
LBE flows in disordered media
8.1.
Flows through porous media
8.2.
LBE flows through porous media
8.3.
Setting up the LBE simulation
8.4.
Deposition algorithm
8.5.
Numerical simulations
8.6.
Synthetic matter and multiscale modeling
8.7.
Exercises
9.
Turbulent flows
9.1.
Fluid turbulence
9.2.
LBE simulations of two-dimensional turbulence
9.3.
Three-dimensional turbulence: parallel performance
9.4.
Three-dimensional channel flow: turbulence
9.5.
Sub-grid scale modeling
9.6.
Summary
9.7.
Exercises
10.
Out of Legoland: geoflexible Lattice Boltzmann Equations
10.1.
Coarse-graining LBE
10.2.
Finite volume LBE
10.3.
Finite difference LBE
10.4.
Interpolation-supplemented LBE
10.5.
Finite element LBE
10.6.
Native LBE schemes on irregular grids
10.7.
Implicit LBE schemes
10.8.
Multiscale lattice Boltzmann scheme
10.9.
Summary
10.10.
Exercises
11.
LBE in the framework of computational fluid dynamics
11.1.
LBE and CFD
11.2.
Link to fully Lagrangian schemes
11.3.
LBE in a nutshell
11.4.
Exercises
III. Beyond fluid dynamics
12.
LBE schemes for complex fluids
12.1.
LBE theory for generalized hydrodynamics
12.2.
LBE schemes for reactive flows
12.3.
LBE schemes for multiphase flows
12.4.
LBE schemes for flows with moving objects
12.5.
Colloidal flows
12.6.
Polymers in LBE flows
12.7.
Snow transport and deposition
12.8.
A new paradigm for non-equilibrium statistical mechanics?
12.9.
New vistas
12.10.
Exercises
13.
LBE for quantum mechanics
13.1.
Quantum mechanics and fluids
13.2.
The fluid formulation of the Schr^d"odinger equation
13.3.
The quantum LBE
13.4.
Numerical tests
13.5.
The quantum N
-body problem
13.6.
Exercises
14.
Thermohydrodynamic LBE schemes
14.1.
Isothemal and athermal lattices
14.2.
Thermodynamic equilibria and multi-energy lattices
14.3.
Extended parametric equilibria
14.4.
Thermal LBE models without nonlinear deviations
14.5.
Reduced thermohydrodynamic schemes
14.6.
Attempts to rescue thermal LBE
14.7.
The Digital Physics approach
14.8.
Fake temperature schemes
14.9.
Summary
14.10.
Exercises
15.
Finale: Who needs LBE?
15.1.
DontUse class
15.2.
CanUse class
15.3.
ShouldUse class
15.4.
MustUse class
16.
Appendices
A.
Integer LBE
B.
The pseudospectral method
C.
A primer on parallel computing
D.
From lattic units to physical units
References
Index
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