Discrete-Ordinates and Streamline Diffusion Methods for a Flow Described by BGK Model

Journal article, 2014

A rarefied gas flow through a channel with arbitrary cross section is studied based on the linearized Bhatnagar-Gross-Krook model. The discrete velocity and streamline diffusion finite element methods are combined to yield a numerical scheme. For this scheme we derive stability and optimal convergence rates in the L-2-type norms. The optimality is due to the maximal available regularity of the exact solution for the corresponding hyperbolic PDE. The potential of the proposed, combined methods is illustrated with some numerical examples.