Radiative Hydrodynamics

Here is how the equation for internal energy is modified due to radiation:

\frac{\partial (\rho e)}{\partial t} = - \kappa_R \rho (4\pi B-cE)

where B=\sigma T^4 is the bolometric Planck function for a blackbody, and 4 \pi B=a T^4, the energy output due to blackbody radiation. cE is the total radiative energy density in the grid, and thus is a sum of blackbody radiation and any additional radiation from radiative sources in the grid.

The equation that governs the total radiative energy in the grid, E,

for the internal energy, and:

for the radiative energy.

The internal energy in the grid can change due to radiation