Changes between Version 19 and Version 20 of FluxLimitedDiffusion

Timestamp:

03/20/13 10:12:58 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -124 +124 @@
 where
 
-[[latex(\Gamma = \frac{dT}{dE} = \frac{(\gamma-1)}{n k_B})]]
+[[latex(\Gamma = \frac{\partial T}{\partial e} = \frac{(\gamma-1)}{n k_B})]]
 
 Then the system of equations becomes
@@ -134 +134 @@
 === 1D ===
 Which we can discretize for (1D) as
+
+||   [[latex(E^{n+1}_i-E^{n}_i = \left [ \alpha^n_{i+1/2} \left ( E^{*}_{i+1}-E^{*}_{i} \right ) - \alpha^n_{i-1/2} \left ( E^{*}_{i}-E^{*}_{i-1} \right ) \right ] + \epsilon^n_i \left ( \frac{4 \pi}{c} B \left ( T^n_i \right ) \left ( 1 - 4\Gamma \frac{e^n_i}{T^n_i} + 4\Gamma \frac{e^{*}_i}{T^n_i} \right ) -E^{*}_i \right ) )]]   ||
+||   [[latex(e^{n+1}_i-e^{n}_i = - \epsilon^n_i \left ( \frac{4 \pi}{c} B\left ( T^n_i \right ) \left ( 1 - 4\Gamma \frac{e^n_i}{T^n_i} + 4\Gamma \frac{e^{*}_i}{T^n_i} \right ) - E^{*}_i \right ) )]]   ||
+
+
+
+
 
 ||   [[latex(E^{n+1}_i-E^{n}_i = \left [ \alpha^n_{i+1/2} \left ( E^{n+1}_{i+1}-E^{n+1}_{i} \right ) - \alpha^n_{i-1/2} \left ( E^{n+1}_{i}-E^{n+1}_{i-1} \right ) \right ] + \epsilon^n_i \left ( \frac{4 \pi}{c} B(T^n_i)-E^{n+1}_i \right ) )]]   ||