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We propose a novel numerical method for solving multi-dimensional, specialrelativistic Boltzmann equations for neutrinos coupled to hydrodynamicsequations. It is meant to be applied to simulations of core-collapsesupernovae. We handle special relativity in a non-conventional way, takingaccount of all orders of v/c. Consistent treatment of advection and collisionterms in the Boltzmann equations is the source of difficulties, which weovercome by employing two different energy grids: Lagrangian remapped andlaboratory fixed grids. We conduct a series of basic tests and perform aone-dimensional simulation of core-collapse, bounce and shock-stall for a15M_{sun} progenitor model with a minimum but essential set of microphysics. Wedemonstrate in the latter simulation that our new code is capable of handlingall phases in core-collapse supernova. For comparison, a non-relativisticsimulation is also conducted with the same code, and we show that they producequalitatively wrong results in neutrino transfer. Finally, we discuss apossible incorporation of general relativistic effects in our method.

Three-dimensional Boltzmann-Hydro code for core-collapse in massive stars I. special relativistic treatments