Changes between Version 12 and Version 13 of u/erica/RadHydro


Ignore:
Timestamp:
03/30/16 09:03:15 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RadHydro

    v12 v13  
    1 '''Radiative Hydrodynamics'''
     1== Radiative Hydrodynamics ==
    22
    33Here is how the internal energy in the grid can change due to radiation:
     
    2121Note the coupling term comes in with a '+' sign now (rightmost term on the RHS), and the diffusion term (left term). Note also that how strongly the matter and radiation couple depends on the opacity.
    2222
    23 ''' Uniform ambient evolution'''
     23== Uniform ambient evolution ==
    2424
    2525The rad. energy in the grid at t=0, assuming no 'sources' is given by the temperature field through the term:
     
    3939There is no change in the radiative energy over time. Now, other dynamics in the simulation, e.g. gravity, could change the temperature distribution in the grid and thus B(T). Only after this would happen, would we begin to see changes in E. Thus, while [[latex($4 \pi B = cE$)]], the system is in radiative equilibrium (right?).
    4040
    41 ''' Jeans unstable gas '''
     41== Jeans unstable gas ==
    4242
    4343Imagine now starting with a uniform, Jeans unstable gas mass. Initially it is in radiative equilibrium (as in previous section), but within a freefall time, the gas will begin to collapse -- becoming denser and hotter as it does (recall equation for internal energy has a gravitational energy term). This will lead to regions in the grid where 4piB>cE. This will increase the radiative energy field,
     
    6565cE needs to get larger than 4piB. This can be achieved by the combined effect of increased BB radiation (through the compressional heating), ''in addition '' to slower diffusion. Thus, for this problem it seems you would want [[latex($\kappa_R= \kappa_R (\rho)$)]]. That is, in the early stages of collapse (low rho), the increased heat due to infall should be cooling through radiative losses. I.e., the collapse should remain isothermal. However, after a certain density is reached, the collapse should become adiabatic. This seems to be controllable through the diffusion term. I can't think of physical reasons why you might want to change [[latex($\kappa_p$)]]. In what situations would you want more or less coupling?
    6666
    67 ''' Radiation with a source '''
     67== Radiation with a source ==
    6868
    6969Now we add a radiating source to the grid.
     70
     71[[Image(radiationdiffusion.png)]]
     72
     73[[Image()]]