The Lattice Gas Model

  In this chapter the lattice gas model is examined. The basic single species models are described as are the attempts at multi-fluid simulations. The derivation of the lattice gas Navier-Stokes equation [8] is outlined and the differences between it and the true Navier-Stokes equation are discussed.. The application of the lattice gas model is also considered.

• Definition of a Lattice Gas Model
• Development of the Lattice Gas Model
  • The HPP Model
  • The FHP Models
    • The FHP-I Model
    • The FHP-II Model
    • The FHP-III Model
    • Other FHP Models
  • Three-Dimensional Models
    • The Multi-Speed Model on a Cubic Lattice
• Boundaries in the Model
• Updating the Lattice
• Equations for the Lattice Gas Model
  • Definitions
  • Microdynamical Equations
  • Macrodynamical Equations
  • Isotropy of the Model
• The Navier-Stokes Equation
• Units of Measurement in a Lattice Gas Model
• Obtaining Macroscopic Quantities
• Binary Fluid Models
  • Introduction to Models with Coloured Particles
  • Properties of Colour Models
  • Surface Tension in a Binary Fluid Model
    • The Reactive Model
    • The Colour-Field Model
• Liquid-Gas Lattice Gas Models
  • The Interactions
  • Implementation of the Interactions
• Lattice Gas Simulations
  • Drawbacks of the Lattice Gas Approach
    • Lack of Galilean Invariance
    • Noisy Results
    • Large Collision Matrices
    • Non-Physical Phase Separation
• Summary
  • Exclusion Principle
  • Galilean Invariance
  • Conservables
  • Isotropy
  • Results for the FHP Models