Mathematisches Kolloquium

Freitag, 10.07.2015 14:15 Uhr

Titel: Physics-based model reduction for the Boltzmann equation

Manuel Torrilhon (RWTH)

The Boltzmann equation describes processes in gases covering regimes from micro-devices to atmospheric re-entry flights. Mathematically it is an integro-differential equation defined for the evolution of the particle distribution in the phase space containing space points and velocities. As such the numerical treatment of the Boltzmann equation remains extremely challenging.

Various approaches exist to reduce the Boltzmann equation to more tractable numerical or physical models. Besides complexity reduction another important aspect of physical models can be paraphrased as 'knowledge extraction': The model equations should allow intuitive insight into the actual process.

We will present a selection of approximation techniques for the Boltzmann equation based on moments of the distribution function, for instance expansions in Hermite functions or using a maximum-entropy approach. As one successful model the regularized 13-moment-equations will be introduced and its discussion combines aspects from partial differential equations, statistics and numerical analysis.

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Ort:  Raum 008/SeMath, Pontdriesch 14-16, 52062 Aachen