Changes between Version 18 and Version 19 of u/erica/RadHydro


Ignore:
Timestamp:
03/30/16 11:37:05 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RadHydro

    v18 v19  
    7171[[Image(DiffusionWave_IC.png, 35%)]]
    7272
    73 For a zone right next to the source,
     73
     74Recall,
    7475
    7576[[latex($\frac{\partial E}{\partial t} = \nabla \cdot (\frac{c \lambda}{\kappa_R \rho} \nabla E) + \kappa_P \rho (4 \pi B - c E)$)]]
    7677
    77 it will acquire some E due to the sink (through the diffusion term), plus through BB radiation (through the coupling term). Here is the grid after the radiative time step:
     78Thus, a zone adjacent to the source will acquire some E due to the sink (through the diffusion term), plus from BB radiation of the ambient medium (through the coupling term). The relative contributions depend on the strengths of the various opacities, as well as the gradient in E. Here is the grid after the radiative time step:
    7879
    7980[[Image(trad.png, 35%)]]
     81
     82The change in E is dominated by the diffusion term closer-in to the sink (strong gradient there), and further away it is dominated by BB radiation.
    8083
    8184Now, depending on position, the internal energy will either decrease or increase. Recall,
     
    8386[[latex($\frac{\partial(\rho e)}{\partial t} = -\kappa_R (4 \pi B - cE)$)]]
    8487
    85 So in close in to the source, E>B, but further away (where diffusion was weaker), B>E. Thus, after a hydro timestep we have:
     88So, close-in to the source, E>B, but further away (where diffusion was weaker), B>E. Thus, after a hydro timestep we have:
    8689
    8790[[Image(thydro.png, 35%)]]