Particle transport and plasmas: models, simulation and applications

Course outline
Rarefied gases
I) Kinetic equations
1) Distribution function
2) Generic form of a kinetic equation
3) Knudsen number
4) Links with hydrodynamic quantities
5) Notion of entropy
6) Equilibrium states
7) BGK model
II) Link with compressible Euler
1) Scaling up scaling
2) Obtaining the Euler equations
3) Entropy problem
III) Discretization of a kinetic equation
1) DVM method
2) Discretization of a kinetic equation
3) Notion of kinetic scheme
Numerical modeling and methods for plasmas
I) Introduction
1) What is a plasma?what is a plasma
2) Magnetic field
II ) Properties
1) Magnetic field
2) Quasi-neutrality
3) Plasma oscillation
III) Euler-Maxwell modelsMaxwell models
1) Notations and units
2) Maxwell's equations
3) Particle density and impulse conservation equations
IV) Vlasov-Maxwell models
1) Vlasov model
2) Vlasov-Poisson model
3) Vlasov-Maxwell model
4) Links with magnetohydrodynamics

Good knowledge of Fortran 90 programming.
Numerical methods for PDEs (finite differences).
Differential and integral calculus.
Fluid mechanics.

Fluid and energetic