Dettagli sull'Insegnamento per l'A.A. 2015/2016

Prerequisiti

Mathematical Analysis, Fourier transform.

Obiettivi

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.

Sillabo

• 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.

Testi di riferimento

• A. N. Gorban, I. V. Karlin,, Invariant MAnifolds for Physical and Chemical Kinetic , Springer, Berlin Heidelberg. (vol. Lect. Notes Phys. 660) 2004..    
• C. Cercignani, The Boltzmann equation and its Applications , Springer-Verlag, New York, . 1988.    

Aggiornamenti alla pagina del corso

• A.A. 2015/2016
• A.A. 2016/2017
• A.A. 2017/2018
• A.A. 2018/2019
• A.A. 2019/2020