Changes between Version 42 and Version 43 of FluxLimitedDiffusion

Timestamp:

03/21/13 11:45:05 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -202 +202 @@
 
 
-If we ignore the change in the Planck function due to heating during the implicit solve, it is equivalent to replacing the term with [[latex(\psi \phi^n_i e^{n+1}_i)]] with [[latex(\psi \phi^n_i e^n_i)]] in which case the equations simplify to
+If we ignore the change in the Planck function due to heating during the implicit solve, it is equivalent to setting [[latex(\bar{\psi} = 1)]] in the term involving [[latex(e^n_i)]] and then setting [[latex(\psi \phi^n_i) = 0]].  This gives the following equation:
 
    [[latex(\left [ 1 + \psi \left( \alpha^n_{i+1/2} + \alpha^n_{i-1/2} + \epsilon^n_i \right ) \right ] E^{n+1}_i - \left ( \psi \alpha^n_{i+1/2} \right ) E^{n+1}_{i+1} - \left ( \psi \alpha^n_{i-1/2} \right ) E^{n+1}_{i-1} =\left [ 1 - \bar{\psi} \left( \alpha^n_{i+1/2} + \alpha^n_{i-1/2} + \epsilon^n_i \right ) \right ] E^n_i+ \left ( \bar{\psi} \alpha^n_{i+1/2} \right ) E^{n}_{i+1} + \left ( \bar{\psi} \alpha^n_{i-1/2} \right ) E^{n}_{i-1} +\phi^n_i e^n_i + \theta^n_i)]]