  In this paper, we apply projective integration methods to hyperbolic moment
models of the Boltzmann equation and the BGK equation, and investigate the
numerical properties of the resulting scheme. Projective integration is an
explicit, asymptotic-preserving scheme that is tailored to problems with large
spectral gaps between slow and (one or many) fast eigenvalue clusters of the
model. The spectral analysis of a linearized moment model clearly shows
spectral gaps and reveals the multi-scale nature of the model for which
projective integration is a matching choice. The combination of the
non-intrusive projective integration method with moment models allows for
accurate, but efficient simulations with significant speedup, as demonstrated
using several 1D and 2D test cases with different collision terms, collision
frequencies and relaxation times.
