The Lattice Boltzmann Equation for Fluid Dynamics and Beyond [Hardcover]

In recent years, certain forms of the Boltzmann equation--now going by the name of Lattice Boltzmann equation (LBE)--have emerged which relinquish most mathematical complexities of the true Boltzmann equation without sacrificing physical fidelity in the description of complex fluid motion. This book provides the first detailed survey of LBE theory and its major applications to date. Accessible to a broad audience of scientists dealing with complex system dynamics, the book also portrays future developments in allied areas of science where fluid motion plays a distinguished role.

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
5.8l³0