Modul

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.

None

• 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

Partial Differential Equations, Functional Analysis