Basic concepts of Lattice Boltzmann Methods

• Summary of basic models
  • Low Mach Navier-Stokes
  • Incompressible Navier-Stokes
  • Advection-Diffusion equations
  • Boundary Conditions (BC)
• Overview of Lattice Boltzmann Methods
  • Continuous Boltzmann equation
  • Discretization of velocity space
  • Lattice Boltzmann Equation (LBE)
  • Equilibrium distribution function
  • Explicit algorithm
  • Chapman-Enskog expansion
  • Variable change in LBE with a source term
  • Bibliography
• Equilibrium distribution functions
• Variable change in LBE for source term
  • Equivalence
  • Bibliography
• Chapman-Enskog expansion for Navier-Stokes equations
  • Starting point
  • Objectives
  • Conservative quantities and moments of equilibrium distribution functions
  • Chapman-Enskog expansion
  • Second part: viscosity coefficient and impulsion balance
  • Récapitulatif
  • Démonstration de l’égalité eq:Equivalence
  • Bibliography