  We develop a numerical code to calculate the neutrino transfer with
multi-energy and multi-angle in three dimensions (3D) for the study of
core-collapse supernovae. The numerical code solves the Boltzmann equations for
neutrino distributions by the discrete-ordinate (S_n) method with a fully
implicit differencing for time advance. The Boltzmann equations are formulated
in the inertial frame with collision terms being evaluated to the zeroth order
of v/c. A basic set of neutrino reactions for three neutrino species is
implemented together with a realistic equation of state of dense matter. The
pair process is included approximately in order to keep the system linear. We
present numerical results for a set of test problems to demonstrate the ability
of the code. The numerical treatments of advection and collision terms are
validated first in the diffusion and free streaming limits. Then we compute
steady neutrino distributions for a background extracted from a spherically
symmetric, general relativistic simulation of 15Msun star and compare them with
the results in the latter computation. We also demonstrate multi-D capabilities
of the 3D code solving neutrino transfers for artificially deformed supernova
cores in 2D and 3D. Formal solutions along neutrino paths are utilized as exact
solutions. We plan to apply this code to the 3D neutrino-radiation
hydrodynamics simulations of supernovae. This is the first article in a series
of reports on the development.
