of 16.3MeV) going outward radially (from top to bottom) on the equator of a supernova core. Generated using the simulation results of [@ott:08]. Inside the protoneutron star ($R \lesssim 30\,\mathrm{km}$) neutrinos and matter are in equilibrium and the radiation field is isotropic. It becomes more and more forward peaked as the neutrinos decouple and become free streaming. Handling the transition from slow diffusion to free streaming correctly requires angle-dependent radiation transport, which is a 6+1 D problem and computationally extremely challenging.[]{data-label="fig:momspace"}](f4.pdf){width="0.8\columnwidth"}

-   **(Magneto)hydrodynamics** (MHD). The stellar plasma is in local thermodynamic equilibrium, essentially perfectly conducting, and essentially inviscid (though neutrinos may provide some shear viscosity in the protoneutron star). The ideal, inviscid MHD approximation is appropriate under these conditions. The MHD equations are hyperbolic and can be written in flux-conservative form with source terms that do not include derivatives of the MHD variables. They are typically solved with standard time-explicit high-resolution shock capturing methods that exploit the characteristic structure of the equations (e.g., [@toro:99]). Special attention must be paid to preserving the divergence-free property of the magnetic field. The MHD equations require an EOS as a closure (see below).

    Unless ultra-strong ($B\gtrsim 10^{15}\,\mathrm{G}$), magnetic fields have little effect on the 