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 $ksim1 h/$Mpc. This technique allows for neutrino memory requirements to be decreased by up to $sim 10^3$ compared to traditional $N$-body methods.
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