Lehrinhalte
From Newtonian mechanics to Liouville and Boltzmann equations, H-theorem, moment methods, asymptotic analysis, non-dimensionalization and scaling regimes, diffusive limit, hydrodynamic limits: Euler and Navier-Stokes equations
Literatur
[list]
[*]Degond: Macroscopic limits of the Boltzmann equation: a review, pp. 3 - 57, in: Modeling and Computational Methods for Kinetic Equations, P. Degond, L. Parschi, G. Russo (eds.), Birkhäuser
[*]Babovsky: Die Boltzmann-Gleichung, Teubner 1998
[*]Saint-Raymond: Hydrodynamic limits of the Boltzmann equation, Springer 2009.
[/list]
Voraussetzungen
recommended: Lecture on Partial differential Equations or similar
Official Course Description
Kinetic equations are an important mathematical tool for many physical, biological, and social applications. Examples are rarefied gases, radiative transfer, transport, or bacterial systems. This lecture starts with the derivation of kinetic equations from "microscopic" models for individual particles or agents. We then investigate general properties of solutions of kinetic equations and discuss approaches for their numerical approximation. Finally, the passage from kinetic to certain "macroscopic" models will be demonstrated. Illuminating observations are a statistical interpretation of the second law of thermodynamics and the fact that the basic laws of fluid dynamics can be traced back to elementary properties of the collision operator in the Boltzmann equation.
From Newtonian mechanics to Liouville and Boltzmann equations, H-theorem, moment methods, asymptotic analysis, non-dimensionalization and scaling regimes, diffusive limit, hydrodynamic limits: Euler and Navier-Stokes equations
Literatur
[list]
[*]Degond: Macroscopic limits of the Boltzmann equation: a review, pp. 3 - 57, in: Modeling and Computational Methods for Kinetic Equations, P. Degond, L. Parschi, G. Russo (eds.), Birkhäuser
[*]Babovsky: Die Boltzmann-Gleichung, Teubner 1998
[*]Saint-Raymond: Hydrodynamic limits of the Boltzmann equation, Springer 2009.
[/list]
Voraussetzungen
recommended: Lecture on Partial differential Equations or similar
Official Course Description
Kinetic equations are an important mathematical tool for many physical, biological, and social applications. Examples are rarefied gases, radiative transfer, transport, or bacterial systems. This lecture starts with the derivation of kinetic equations from "microscopic" models for individual particles or agents. We then investigate general properties of solutions of kinetic equations and discuss approaches for their numerical approximation. Finally, the passage from kinetic to certain "macroscopic" models will be demonstrated. Illuminating observations are a statistical interpretation of the second law of thermodynamics and the fact that the basic laws of fluid dynamics can be traced back to elementary properties of the collision operator in the Boltzmann equation.
- Lehrende: Herbert Egger
- Lehrende: Jan Giesselmann
Semester: WT 2018/19