Interfacial Standing Wave Simulations

  It has been seen in chapters 4 and 5 that a lattice Boltzmann model can be used to simulate two immiscible binary fluids and that a gravitational interaction can be introduced into the lattice Boltzmann scheme. It has been shown that the immiscible, binary fluid model of Orlandini et al. [9] is isotropic and that the gravitational interactions are independent of the grid orientation. The combination of the two is, at worst, very close to Galilean invariant for the correct choice of . This model is therefore suitable for modelling interfacial waves.

• The density Gradient, the Potential Density, the Relative Density and the Gravitational Strength
• Standing Wave Initialisation
• Standing Wave Simulations
• The Wave Period and the Damping Parameter
  • The Curve Fitting Process
    • The Contribution to e from the Discrete Lattice
    • Relating the Error Parameter to an Error in the Fitted Parameters
    • Curve Fitting Results
  • Comparison with Theory
  • Continuously Varying Density at the Interface
• Velocities
  • Velocity Variation Across a Vertical Cross-Section
  • Velocity Variation Across a Horizontal Cross-Section
  • Boundary Layer at the Solid Boundaries
  • Peak Horizontal Velocity
• Summary