  The cosmic neutrino background is an important component of the Universe that
is difficult to include in cosmological simulations due to the extremely large
velocity dispersion of neutrino particles. We develop a new approach to
simulate cosmic neutrinos that decomposes the Fermi-Dirac phase space into
shells of constant speed and then evolves those shells using hydrodynamic
equations. These collisionless hydrodynamic equations are chosen to match
linear theory, free particle evolution and allow for superposition. We
implement this method into the information-optimized cosmological $N$-body code
CUBE and demonstrate that neutrino perturbations can be accurately resolved to
at least $k\sim1\ h/$Mpc. This technique allows for neutrino memory
requirements to be decreased by up to $\sim 10^3$ compared to traditional
$N$-body methods.
