Convergence of Moment Methods for Linear Kinetic Equations

Numerical methods for linear kinetic equations based on moment expansions for a discretization in the velocity direction are examined. The moment equations are hyperbolic systems which can be shown to converge to the kinetic equation as the order of the expansion tends to infinity and to a drift-diffusion model as the Knudsen number tends to zero. A discretization of the moment equations with respect to time and space is presented, a stability result is proven, and some aspects of an implementation are discussed. In particular, an adaptive procedure is described where the order of the expansion is determined locally. Results of numerical experiments are presented.