Time evolution of far-field neutrino rms energies observed in the fluid comoving frame ﹩\sqrt{\langle {{\epsilon }_{{\nu }_{l}}}^{2}\rangle }﹩ (left panel) and luminosities ﹩{L}_{{\nu }_{l}}^{\mathrm{Euler}}﹩ (right panel) measured by an Eulerian observer at 500 km of a collapsing 20 M _⊙ star. The dashed–dotted lines, dashed lines, and solid lines correspond to the results of Con, Adv.I, and Adv.II, respectively. The neutrino luminosities and rms energy values in Adv.I and Adv.II show significant differences compared to Con. For instance, at a time of t − t _bounce = 70 ms, the results of Adv.II have relative differences of ﹩\left[+5.7 \% ,+12.7 \% ,+7.8 \% \right]﹩ (﹩+7.9 \% ,+13.1 \% ,+47.8 \% ﹩) in the values of ﹩\sqrt{\langle {{\epsilon }_{{\nu }_{l}}}^{2}\rangle }﹩ (﹩{L}_{{\nu }_{l}}^{\mathrm{Euler}}﹩) for the neutrino species ﹩\left[{\nu }_{e},{\bar{\nu }}_{e},{\nu }_{x}\right]﹩ when compared to the results of Con.