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We report on the core-collapse supernova simulation we conducted for a 11.2 Mprogenitor model in three-dimensional space up to 20 ms after bounce, using aradiation hydrodynamics code with full Boltzmann neutrino transport. We solvethe six-dimensional Boltzmann equations for three neutrino species and thethree-dimensional compressible Euler equations with Furusawa and Togashi'snuclear equation of state. We focus on the prompt convection at 10 ms afterbounce and investigate how neutrinos are transported in the convective matter.We apply a new analysis based on the eigenvalues and eigenvectors of theEddington tensor and make a comparison between the Boltzmann transport resultsand the M1 closure approximation in the transition regime between the opticallythick and thin limits. We visualize the eigenvalues and eigenvectors using anellipsoid, in which each principal axis is parallel to one of the eigenvectorsand has a length proportional to the corresponding eigenvalue. This approachenables us to understand the difference between the Eddington tensor deriveddirectly from the Boltzmann simulation and the one given by the M1 prescriptionfrom a new perspective. We find that the longest principal axis of theellipsoid is almost always nearly parallel to the energy flux in the M1 closureapproximation whereas in the Boltzmann simulation it becomes perpendicular insome transition regions, where the mean free path is 0.1 times the radius. Inthree spatial dimensions, the convective motions make it difficult to predictwhere this happens and to possibly improve the closure relation there.

Simulations of the Early Post-Bounce Phase of Core-Collapse Supernovae in Three-Dimensional Space with Full Boltzmann Neutrino Transport