Mathematical Analysis, Fourier transform.
This course provides an introduction to the classical kinetic theory of gases and the principles of kinetic modeling.
A special focus is given to the derivation of hydrodynamic equations from kinetic models by means of non-perturbative techniques and to the analysis of numerical schemes for the simulation of fluid flows.
On successful completion of this module the student has the knowledge on the basic principles and the simulation strategies of kinetic models.
Boltzmann equation and the principles of kinetic description.
Kinetic models: BGK,Maxwell molecules, Vlasov equation and Fokker-Planck equation.
The closure problem and methods of reduced description: Chapman-Enskog expansion, Grad's Moment method.
Non-perturbative techniques in kinetic theory: the method of the slow invariant manifold.
Overview on Lattice Boltzmann models.
Monte Carlo simulations of lattice gas models.