Changes between Version 85 and Version 86 of FluxLimitedDiffusion

Timestamp:

03/27/13 22:40:20 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -446 +446 @@
 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 E^{*}_i  + \phi^n_i e^{*}_i  + \theta^n_i) - \omega_{x,i} v_{x,i} \left ( E^{*}_{i+1}-E^*_{i-1} \right ) )]]   
-   [[latex(e^{n+1}_i-e^{n}_i = \epsilon^n_i E^{*}_i  - \phi^n_i e^{*}_i  - \theta^n_i + \omega_{x,i} v_{x,i} \left ( E^{*}_{i+1}-E^*_{i-1} \right ) )]]   
+   [[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 E^{*}_i  + \phi^n_i e^{*}_i  + \theta^n_i) - \omega_{i} v_{x,i} \left ( E^{*}_{i+1}-E^*_{i-1} \right ) )]]   
+   [[latex(e^{n+1}_i-e^{n}_i = \epsilon^n_i E^{*}_i  - \phi^n_i e^{*}_i  - \theta^n_i + \omega_{i} v_{x,i} \left ( E^{*}_{i+1}-E^*_{i-1} \right ) )]]   
 
 where the diffusion coefficient is given by 
@@ -471 +471 @@
 and
 
-where [[latex(\omega_{x,i} = \frac{\Delta t}{\Delta x} \lambda_i \left ( \frac{\kappa_{0P},i}{\kappa_{0R,i}}-\frac{1}{2} \right ) )]]
+where [[latex(\omega_{i} = \frac{\Delta t}{\Delta x} \lambda_i \left ( \frac{\kappa_{0P},i}{\kappa_{0R,i}}-\frac{1}{2} \right ) )]]
 
 and we can think of the radiative flux as