| | 218 | === Flux limiting === |
| | 219 | Limiting the fluxes in the explicit case is not too difficult, however in the implicit case, we cannot limit the flux directly, but must instead, limit the conductivities. |
| | 220 | |
| | 221 | $n \chi_\parallel \hat{b} \cdot \nabla T < 5 \phi \rho c_s^3 \rightarrow \chi_\parallel < \frac{5 \phi \rho c_s^3}{n \hat{b} \cdot \nabla T} \equiv \chi_{\max}$ |
| | 222 | |
| | 223 | We can limit $\chi$ using $\chi = \min{\left ( \chi, \chi_{\max} \right )}$ or do something like |
| | 224 | |
| | 225 | $\chi = \chi_{\max} \tanh \frac{\chi}{\chi_{\max}}$ |
| | 226 | |
| | 227 | |
| | 228 | |
