Changes between Version 1 and Version 2 of u/erica/RadHydro


Ignore:
Timestamp:
03/29/16 16:18:32 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RadHydro

    v1 v2  
    55[[latex($\frac{\partial (\rho e)}{\partial t} = - \kappa_R \rho (4\pi B-cE)$)]]
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    7 where [[latex($B=\sigma T^4$)]] is the bolometric Planck function for a blackbody, and [[latex($4 \pi B=a T^4$)]], the energy output due to blackbody radiation. [[latex($cE$)]] 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.
     7where [[latex($B=\sigma T^4$)]] is the bolometric Planck function for a blackbody (BB), and [[latex($4 \pi B=a T^4$)]] is the energy output due to BB radiation. [[latex($cE$)]] is the radiative energy density in the grid. This equation shows that when [[latex($4 \pi B > cE$)]],
    88
    9 The equation that governs the total radiative energy in the grid, E,
     9[[latex($\frac{\partial \rho e}{\partial t}<0$)]]
     10
     11which is interpreted as the matter losing energy via BB radiation. That is, the internal energy of that zone will decrease, thereby producing a concomitant increase in the radiation field's energy, or E, as we will see next. This equation also tells us that when [[latex($4 \pi B<cE$)]], 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,
     12
     13[[latex($\frac{\partial \rho e}{\partial t}>0$)]]
     14
     15Since the matter and the radiation are coupled in this way, the equation that governs the total radiative energy in the grid is the inverse of the internal energy, but with an added term for diffusion. Thus, E, can change in the grid either by acquiring energy from the blackbody radiation, and/or, by diffusion. 
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