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Simulation of the cosmic clustering of massive neutrinos is a daunting task, due both to their large velocity dispersion and to their weak clustering power becoming swamped by Poisson shot noise. We present a new approach, the multi-fluid hybrid-neutrino simulation, which partitions the neutrino population into multiple flows, each of which is characterised by its initial momentum and treated as a separate fluid. These fluid flows respond initially linearly to nonlinear perturbations in the cold matter, but slowest flows are later converted to a particle realisation should their clustering power exceed some threshold. After outlining the multi-fluid description of neutrinos, we study the conversion of the individual flows into particles, in order to quantify transient errors, as well as to determine a set of criteria for particle conversion. Assembling our results into a total neutrino power spectrum, we demonstrate that our multi-fluid hybrid-neutrino simulation is convergent to $<3\%$ if conversion happens at $z=19$ and agrees with more expensive simulations in the literature for neutrino fractions as high as $Ω_νh^2 = 0.005$. Moreover, our hybrid-neutrino approach retains fine-grained information about the neutrinos' momentum distribution. However, the momentum resolution is currently limited by free-streaming transients excited by missing information in the neutrino particle initialisation procedure, which restricts the particle conversion to z $\gtrsim 19$ if percent-level resolution is desired.