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This is a status report on our endeavor to reveal the mechanism ofcore-collapse supernovae (CCSNe) by large-scale numerical simulations.Multi-dimensionality of the supernova engine, general relativisticmagnetohydrodynamics, energy and lepton number transport by neutrinos emittedfrom the forming neutron star as well as nuclear interactions there, are allbelieved to play crucial roles in repelling infalling matter and producingenergetic explosions. These ingredients are nonlinearly coupled with oneanother in the dynamics of core-collapse, bounce, and shock expansion. Seriousquantitative studies of CCSNe hence make extensive numerical computationsmandatory. Since neutrinos are neither in thermal nor in chemical equilibriumin general, their distributions in the phase space should be computed. This isa six dimensional (6D) neutrino transport problem and quite a challenge evenfor those with an access to the most advanced numerical resources such as the"K computer". To tackle this problem, we have embarked on multi-front efforts.In particular we report in this paper our recent progresses in the treatmentsof multi-dimensional (multi-D) radiation-hydrodynamics. We are currentlyproceeding on two different paths to the ultimate goal; in one approach weemploy an approximate but highly efficient scheme for neutrino transport andtreat 3D hydrodynamics and/or general relativity rigorously; someneutrino-driven explosions will be presented and comparisons will be madebetween 2D and 3D models quantitatively; in the second approach, on the otherhand, exact but so far Newtonian Boltzmann equations are solved in two andthree spatial dimensions; we will show some demonstrative test simulations. Wewill also address the perspectives of exa-scale computations on the nextgeneration supercomputers.

Core-Collapse Supernovae as Supercomputing Science: a status report  toward 6D simulations with exact Boltzmann neutrino transport in full general  relativity