PART V: course reminders

Lattice Boltzmann Methods

• Basic concepts of Lattice Boltzmann Methods
  • Overview of Lattice Boltzmann Methods
  • Equilibrium distribution functions
  • Equilibrium distribution functions for incompressible Navier-Stokes equations
  • Equilibrium distribution functions for Transport equations
  • Variable change in LBE for source term
  • Chapman-Enskog expansion for Navier-Stokes equations

Phase-field theory

• Basic concepts of phase-field theory: two-phase
  • Principe de moindre action
  • Fundamentals of phase-field theory
  • Time-evolution: Cahn-Hilliard and Allen-Cahn models
  • Derivation of incompressible Navier-Stokes with interface-capturing equation model
  • Contact angle

Phase-field models for phase transition

• Phase-field models for phase transition
  • Model of solidification and crystal growth
  • Isothermal Navier-Stokes/Korteweg model
  • Mass transfer through interfaces
  • Incompressible Liquid/gas phase change