wiki:u/erica/scratch3

Version 5 (modified by Erica Kaminski, 9 years ago) ( diff )

is the 'flux limiter'. It comes into the equations in the diffusion term:

This is because instead of solving the following conservation equation,

(which would require an additional equation for F), we make the 'flux-limited' approximation that,

This then turns the conservation equation into a diffusion equation:

The value of controls whether the radiation is diffusing in the free-streaming limit (), i.e. at the speed of light, or is diffusing as it would in the optically thick limit (). The FLD approximation does well at these two limits, but not in between. Let's examine these two limits in more detail and then consider why it doesn't perform as well in between. Here is the functional form of ,

where,

Graphically, we have:

Optically thick limit

And we see that as , . How to interpret this? R is essentially the ratio of the optical depth , to the radiation's scale height, .

Thus, as , we have that - i.e. radiation travels infinitesmally small distances before it is absorbed or scattered - and thus, we are in the optically thick regime.

The rad diffusion equation then becomes,

which is equation 6.59 in Drake's book.

Free streaming limit

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