3. Lattice-gas cellular automata

Abstract

• 3.1 The HPP lattice-gas cellular automata

  • 3.1.1 Model description

  • 3.1.2 Implementation of the HPP model: How to code lattice-gas cellular automata?

  • 3.1.3 Initialization

  • 3.1.4 Coarse graining

• 3.2 The FHP lattice-gas cellular automata

  • 3.2.1 The lattice and the collision rules

  • 3.2.2 Microdynamics of the FHP model

  • 3.2.3 The Liouville equation

  • 3.2.4 Mass and momentum density

  • 3.2.5 Equilibrium mean occupation numbers

  • 3.2.6 Derivation of the macroscopic equations: multi-scale analysis

  • 3.2.7 Boundary conditions

  • 3.2.8 Inclusion of body forces

  • 3.2.9 Numerical experiments with FHP

  • 3.2.10 The 8-bit FHP model

• 3.3 Lattice tensors and isotropy in the macroscopic limit

  • 3.3.1 Isotropic tensors

  • 3.3.2 Lattice tensors: single-speed models

  • 3.3.3 Generalized lattice tensors for multi-speed models

  • 3.3.4 Thermal LBMs: D2Q13-FHP (multi-speed FHP model)

  • 3.3.5 Exercises

• 3.4 Desperately seeking a lattice for simulations in three dimensions

  • 3.4.1 Three dimensions

  • 3.4.2 Five and higher dimensions

  • 3.4.3 Four dimensions

• 3.5 FCHC

  • 3.5.1 Isometric collision rules for FCHC by Hénon

  • 3.5.2 FCHC, computers and modified collision rules

  • 3.5.3 Isometric rules for HPP and FHP

  • 3.5.4 What else?

• 3.6 The pair interaction (PI) lattice-gas cellular automata

  • 3.6.1 Lattice, cells, and interaction in 2D

  • 3.6.2 Macroscopic equations

  • 3.6.3 Comparison of PI with FHP and FCHC

  • 3.6.4 The collision operator and propagation in C and FORTRAN

• 3.7 Multi-speed and thermal lattice-gas cellular automata

  • 3.7.1 The D3Q19 model

  • 3.7.2 The D2Q9 model

  • 3.7.3 The D2Q21 model

  • 3.7.4 Transsonic and supersonic flows: D2Q25, D2Q57, D2Q129

• 3.8 Zanetti (‘staggered’) invariants

  • 3.8.1 FHP

  • 3.8.2 Significance of the Zanetti invariants

• 3.9 Lattice-gas cellular automata: What else?