Gravity in a Lattice Boltzmann Model

  In this chapter different methods are considered for introducing a body force, in this case gravity, into a lattice Boltzmann model. A new method is proposed which introduces the body force directly into the lattice Boltzmann equation. This is compared with the method of Martys et al. [66]. It is shown that when the new body force rules are incorporated into an isotropic model the body force acts independently of the grid orientation. It is also shown that when the body force is introduced into the Galilean invariant, binary model of Orlandini et al. [9] the resulting model is also Galilean invariant.

• Introducing Gravity
  • The Classic Boltzmann Equation
  • Combining the Gravity Term and the Pressure Tensor
  • Adding a Force Term to Equation ()
  • Calculating the Equilibrium Distribution with an Altered Velocity
  • Adding an Additional Term to the Boltzmann Equation
  • Review of Methods
• Model Implementation
  • Density Gradient
  • Model Comparison
  • Grid Orientation
    • Results
  • Gravitational Strength
    • Single Species Model
    • Immiscible Binary Fluid
• Galilean Invariance
• Summary