PART V: course reminders

• Fluid dynamics & Thermodynamics
  • Navier-Stokes equations for single-phase flows
  • Energy balance equation
  • Principe de moindre action
• Introduction of two-phase flows
  • Scales and approaches (to be written)
  • Local and instantaneous Navier-Stokes equations
  • Overview of interface-tracking methods with one-fluid formulation (to be completed)
  • Analytical solutions for two-phase
• Basic concepts of Lattice Boltzmann Methods
  • Summary of basic models
  • Overview of Lattice Boltzmann Methods
  • Equilibrium distribution functions
  • Variable change in LBE for source term
  • Chapman-Enskog expansion for Navier-Stokes equations
• Basic concepts of phase-field theory: two-phase
  • Fundamentals of phase-field theory
  • Time-evolution: Cahn-Hilliard and Allen-Cahn models
  • Model of incompressible Navier-Stokes with interface-capturing equation
  • Isothermal Navier-Stokes/Korteweg model
  • Thermodynamics of phase transition (to be written)