Changes between Version 12 and Version 13 of u/erica/RadHydro
- Timestamp:
- 03/30/16 09:03:15 (9 years ago)
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u/erica/RadHydro
v12 v13 1 '''Radiative Hydrodynamics''' 1 == Radiative Hydrodynamics == 2 2 3 3 Here is how the internal energy in the grid can change due to radiation: … … 21 21 Note 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. 22 22 23 ''' Uniform ambient evolution''' 23 == Uniform ambient evolution == 24 24 25 25 The rad. energy in the grid at t=0, assuming no 'sources' is given by the temperature field through the term: … … 39 39 There 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?). 40 40 41 ''' Jeans unstable gas ''' 41 == Jeans unstable gas == 42 42 43 43 Imagine 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, … … 65 65 cE 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? 66 66 67 ''' Radiation with a source ''' 67 == Radiation with a source == 68 68 69 69 Now we add a radiating source to the grid. 70 71 [[Image(radiationdiffusion.png)]] 72 73 [[Image()]]