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An advanced class on mathematical modeling of gas flows in rarefied or diluted processes.

Intention

The Navier-Stokes equation fails when there are not enough particle interaction, that is, the ratio between mean free path of the particle and the observation scale (= Knudsen number) is too large. We discuss enhanced/extended fluid mechanics based on kinetic gas theory / Boltzmann equation. These equations are applicable for moderate Knudsen-number processes, like in rarefied or microscopic settings. Special focus will be the theory of regularized 13-moment-equations (R13 System).

Info

The formal structure of the class will be 2 hours of lectures and 1 hour of tutorial each week. The tutorials will be merged into 2 hours every other week.

The times for lectures and tutorials are given below.

• Friday, 10:30-12:00, 1090(Rogowski)|328
  (lecture, starting 13 Oct)
• Wednesday, 12:30 - 14:00, in 1090(Rogowski)|328
  (bi-weekly exercise, starting 18 Oct)

There are 5 ECTS points to earn with an oral exam of 30min.

See also online.rwth-aachen.de. Please register with the course to gain access to the Moodle-Page.

Some Background Literature

The course will be based on a short course Kinetic Theory of Non-Equilibrium Gas Flows: Theory and Computations (pdf) which can be seen as an extension of the book:

• H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Springer, New York (2005).

Below is a list of further references. These items is not meant to cover the course as they actually go far beyond the course material. But they certainly resonate with what is done in the course.

• S. R. De Groot & P. Mazur, Irreversible Thermodynamics, Dover, 1962
• S. Chapman & T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd ed., Cambridge University Press, 1970
• I. Müller & T. Ruggeri, Rational Extended Thermodynamics, Springer New York, March 2013
• G. M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases, Springer Berlin Heidelberg, 2010