On half-space problems for the linearized discrete Boltzmann equation
Received: 19 May 2008 Revised: 10 November 2008
Mathematics Subject Classification (2000): 82C40 - 76P05
This research was partially supported by the Swedish Research Council grant 2003-5357.
Abstract In this paper we study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for the discrete Boltzmann equation. The discrete Boltzmann equation reduces to a system of ODEs for plane stationary problems. These systems are studied, and for general boundary conditions at the "wall" a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete Boltzmann equation is made. Applications for axially symmetric models are studied in more detail. Exact solutions of a (simplified) linearized kinetic model of BGK type are also found as a limiting case of the corresponding discrete models.