**W. KOLLER** and **F. SCHURRER**

*Conservative solution methods for extended Boltzmann equations*

**Pages:** 109-169

**Received:** 12 February 2001

**Mathematics Subject Classification (2000):** 82C40

**Abstract**:
We review current strategies of energy discretization
of the Boltzmann equation in the framework of extended kinetic
theory. When external fields can be neglected, the semi - continuous
Boltzmann equation yields a sound basis for various
application. A three component gas mixture interacting with monochromatic
photons as well as a four component gas mixture undergoing chemical
reactions are dealt with by means of this approach. The model equations
reflect all major aspects of a continuous kinetic description, such as,
consevation laws, equilibria and an H - theorem.
Spatially dependent problems are treated by applying an expansion of the
distribution function in terms of Legendre polynomials with respect to the
polar angle. The resulting PDE in real space and time are solved by an
implicit finite differencing scheme combined with an operator splitting
method.
In the presence of external fields, an overlapping multigroup method
(with a spline - interpolation method as its extension ) is developed for
numerical studies. Furthermore, a formulation of a multigroup approach
consistent with the non - linear Boltzmann equation is presented.

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