18 | | The value of [[latex($\lambda$)]] controls whether the radiation is diffusing in the free-streaming limit ([[latex($\lambda \rightarrow 0$)]]), i.e. at the speed of light, or is diffusing as it would in the optically thick limit ([[latex($\lambda \rightarrow \frac {1}{3}$)]]). 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. |
| 18 | The value of [[latex($\lambda$)]] controls whether the radiation is diffusing in the free-streaming limit ([[latex($\lambda \rightarrow 0$)]]), i.e. at the speed of light, or is diffusing as it would in the optically thick limit ([[latex($\lambda \rightarrow \frac {1}{3}$)]]). 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 [[latex($\lambda$)]], |
| 19 | |
| 20 | [[latex($\lambda = \frac{1}{R}(\coth{R}-\frac{1}{R})$)]] |
| 21 | |
| 22 | where, |
| 23 | |
| 24 | [[latex($R=|\frac{\nabla E}{\kappa_R \rho E}|$)]] |
| 25 | |
| 26 | Graphically, we have [[latex($\lambda$)]] |
| 27 | |
| 28 | [[Image(fld.png, 35%)]] |