  Fluid dynamical simulations are often performed using cheap macroscopic
models like the Euler equations. For rarefied gases under near-equilibrium
conditions, however, macroscopic models are not sufficiently accurate and a
simulation using more accurate microscopic models is often expensive. In this
paper, we introduce a hierarchical micro-macro acceleration based on moment
models that combines the speed of macroscopic models and the accuracy of
microscopic models. The hierarchical micro-macro acceleration is based on a
flexible four step procedure including a micro step, restriction step, macro
step, and matching step. We derive several new micro-macro methods from that
and compare to existing methods. In 1D and 2D test cases, the new methods
achieve high accuracy and a large speedup.
