two. Hence, in a 3D simulation, the computational cost scales with the fourth power of resolution.

Multi Scale
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Taking the red supergiant in Figure \[fig:collapse\] as an example, a complete core-collapse supernova simulation that follows the shock to the stellar surface, would have to cover dynamics on a physical scale from $\sim$$10^9\,\mathrm{km}$ (stellar radius) down to $\sim$$0.1\,\mathrm{km}$ (the typical scale over which structure and thermodynamics of the protoneutron star change). These ten orders of magnitude in spatial scale are daunting. In practice, reviving the shock and tracking its propagation to the surface can be treated as (almost) independent problems. If our interest is on the shock revival mechanism, we need to include the inner $\sim$$10,000\,\mathrm{km}$ of the star. Since information about core collapse is communicated to overlying layers with the speed of sound, stellar material at greater radii will not “know” that core collapse has occurred before it is hit by the revived expanding shock.

Even with only five decades in spatial scale, some form of grid refinement or adaptivity is called for: a 3D finite-difference grid with an extent of $10,000\,\mathrm{km}$ symmetric about the origin with uniform $0.1\,\mathrm{km}$ cell size would require 57 PB of RAM to store 