W. KOLLER and F. SCHURRER
Conservative solution methods for extended Boltzmann equations
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.