Modul
Introduction to Kinetic Theory [M-MATH-103919]
Credits
4Recurrence
Jedes WintersemesterDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-108013 | Introduction to Kinetic Theory | 4 |
Competence Goal
After successfully taking part in the module’s classes and exams, students have gained knowledge and abilities as described in the “Inhalt” section. Specifically, Students know common means of mesoscopic and macroscopic description of particle systems. Furthermore, students are able to describe the basics of multiscale methods, such as the asypmtotic analysis and the method of moments. Students are able to apply numerical methods to solve engineering problems related to particle systems. They can name the assumptions that are needed to be made in the process. Students can judge whether specific models are applicable to the specific problem and discuss their results with specialists and colleagues.
Prerequisites
None
Content
- From Newton's equations to Boltzmann's equation
- Rigorous derivation of the linear Boltzmann equation
- Properties of kinetic equations (existence & uniqueness, H theorem)
- The diffusion limit
- From Boltzmann to Euler & Navier-Stokes
- Method of Moments
- Closure techniques
- Selected numerical methods
Recommendation
Partial Differential Equations, Functional Analysis