wiki:u/erica/RadHydro

Version 3 (modified by Erica Kaminski, 9 years ago) ( diff )

Radiative Hydrodynamics

Here is how the internal energy in the grid can change due to radiation:

where is the bolometric Planck function for a blackbody (BB), and is the energy output due to BB radiation. is the radiative energy density in the grid. This equation shows that when ,

which is interpreted as the matter losing energy via BB radiation. That is, the internal energy of that zone will decrease, having been transferred into radiative energy. This equation also tells us that when , there is more energy in the radiation field than in the BB, and so it gets absorbed by the matter. This causes the internal energy to increase,

Changes to the internal energy lead to changes in temperature, and thus the next time step the amount of radiative energy from the BB will change (recall B=B(T)).

Now, since the matter and the radiation are coupled in this way, the equation that governs the radiative energy in the grid is the inverse of the internal energy. Additionally, the radiative energy can diffuse through the grid, so there is an extra term for diffusion:

for the internal energy, and:

for the radiative energy.

The internal energy in the grid can change due to radiation

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