at 10 ms after bounce by introducing random perturbations of $1\%$ in velocity behind the stalled shock.

To test the sensitivity of the supernova dynamics to numerical resolutions, we compute 3D model-series with lower angular resolutions, namely half or quarter of the (equidistant) mesh numbers in the azimuthal direction ($n_r \times n_{\theta} \times
 n_{\phi}$ = $320 \times 64 \times 64$ and $n_r \times n_{\theta} \times n_{\phi}$ = $320 \times 64 \times 32$). In 2D simulations we vary the mesh numbers in the lateral direction as $n_r \times n_{\theta} $ = $320 \times 64$, $n_r \times n_{\theta} $ = $320 \times 128$ and $n_r \times n_{\theta} $ = $320 \times 256$, respectively (see Table 1). In the table, model 3D-H-1 differs from model 3D-H-2 (and 3D-H-3 etc) only in the random seed perturbations (with the perturbation amplitudes being the same in all cases). Note that the lowest-resolution 3D model in this work corresponds to the best-resolution model in @takiwaki12. By using the fastest [*K*]{} computer in Japan, it took typically 1.3 months (equivalently $\sim$ 4 million core-hour computing-time) for each of our 3D fiducial models.

[lccccccccccccc]{} 3D-H-1 & $ 320 \times 64 \times 128 $ & $ 2.8^{\circ} \times  2.8^{\circ} $ 