a single double precision variable. Many tens to hundreds of 3D variables are required. Such high uniform resolution is not only currently impossible but also unnecessary. Most of the resolution is needed near the protoneutron star and in the region behind the stalled shock. The near-free-fall collapse of the outer core can be simulated with much lower resolution.

Because of the broad range of physics involved (see below) and the limited available compute power, early core-collapse supernova simulations were spherically symmetric (1D). 1D simulations often employ a Lagrangian, comoving mass coordinate discretization. This grid can be set up to provide just the right resolution where and when needed or can be dynamically re-zoned (an adaptive mesh refinement \[AMR\] technique). Other 1D codes discretize in the Eulerian frame and use a fixed grid whose cells are radially stretched using geometric progression.

In 2D simulations, Eulerian, geometrically-spaced fixed spherical grids are the norm, but some codes use cylindrical coordinates and AMR. Spherical grids, already in 2D, suffer from a coordinate singularity at the axis that can lead to numerical artifacts. In 3D, they become even more difficult to handle and their focusing grid lines impose a severe timestep constraint near the origin. 