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In this paper the non-linear effect of massive neutrinos on cosmologicalstructures is studied in a conceptually new way. We have solved the non-linearcontinuity and Euler equations for the neutrinos on a grid in real space in$N$-body simulations, and closed the Boltzmann hierarchy at the non-linearEuler equation using the stress and pressure perturbations from linear theory.By comparing with state-of-the art cosmological neutrino simulations, we areable to simulate the non-linear neutrino power spectrum very accurately. Thistranslates into a negligible error in the matter power spectrum, and so our$\scriptstyle{\rm CO}N{\rm CEPT}$ code is ideally suited for extracting theneutrino mass from future high precision non-linear observational probes suchas Euclid.

$\nu\scriptstyle{\rm CO}N{\rm CEPT}$: Cosmological neutrino simulations from the non-linear Boltzmann hierarchy