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We present numerical results on three-dimensional (3D) hydrodynamiccore-collapse simulations of an $11.2 M_{\odot}$ star. By comparing one-(1D)and two-dimensional(2D) results with those of 3D, we study how the increasingspacial multi-dimensionality affects the postbounce supernova dynamics. Thecalculations were performed with an energy-dependent treatment of the neutrinotransport that is solved by the isotropic diffusion source approximationscheme. By performing a tracer-particle analysis, we show that the maximumresidency time of material in the gain region is shown to be longer for 3D dueto non-axisymmetric flow motions than 2D, which is one of advantageous aspectsof 3D models to obtain neutrino-driven explosions. Our results show thatconvective matter motions below the gain radius become much more violent in 3Dthan 2D, making the neutrino luminosity larger for 3D. Nevertheless the emittedneutrino energies are made smaller due to the enhanced cooling. Our resultsindicate whether these advantages for driving 3D explosions could or could notoverwhelm the disadvantages is sensitive to the employed numerical resolutions.An encouraging finding is that the shock expansion tends to become moreenergetic for models with finer resolutions. To draw a robust conclusion, 3Dsimulations with much more higher numerical resolutions and also with moreadvanced treatment of neutrino transport as well as of gravity is needed, whichcould be hopefully practicable by utilizing forthcoming Petaflops-classsupercomputers.

Three-dimensional Hydrodynamic Core-Collapse Supernova Simulations for an $11.2 M_{\odot}$ Star with Spectral Neutrino Transport