Changes between Version 23 and Version 24 of FluxLimitedDiffusion

Timestamp:

03/20/13 11:48:16 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -178 +178 @@
 In any event in 1D we have the following matrix coefficients
 
-||   [[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 ( \psi \phi^n_i \right ) e^{n+1}_i=\left [ 1 - \bar{\psi} \left( \alpha^n_{i+1/2} + \alpha^n_{i-1/2} + \epsilon^n_i \right ) \right ] E^n_i+\bar{\psi}\phi e^n_i + \theta^n_i)]]   ||
-||   [[latex(\left ( 1 +\psi \phi \right ) e^{n+1}_i - \left ( \psi \epsilon^n_i \right )E^{n+1}_i =\left ( 1 - \bar{\psi} \right ) e^n_i + \left ( \bar{\psi} \epsilon^n_i \right ) E^n_i-theta^i_n )]]   ||
+||   [[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 ( \psi \phi^n_i \right ) e^{n+1}_i=\left [ 1 - \bar{\psi} \left( \alpha^n_{i+1/2} + \alpha^n_{i-1/2} + \epsilon^n_i \right ) \right ] E^n_i+\bar{\psi}\phi^n_i e^n_i + \theta^n_i)]]   ||
+||   [[latex(\left ( 1 +\psi \phi^n_i \right ) e^{n+1}_i - \left ( \psi \epsilon^n_i \right )E^{n+1}_i =\left ( 1 - \bar{\psi}\phi^n_i \right ) e^n_i + \left ( \bar{\psi} \epsilon^n_i \right ) E^n_i-\theta^i_n )]]   ||
+
+
 
 Clearly the second equation is trivial to solve after the first system of equations has been solved.  So if we treat the temperature as being constant we can calculate the local heating/cooling due to radiative emission/absorption