Changes between Version 136 and Version 137 of FluxLimitedDiffusion

Timestamp:

03/31/13 10:52:15 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -467 +467 @@
 \begin{eqnarray}
 E^{n+1}_i-E^{n}_i = & \left [ \alpha^n_{i+1/2} \left ( \psi E^{n+1}_{i+1} + \bar{\psi} E^{n}_{i+1}- \psi E^{n+1}_{i} - \bar{\psi} E^n_{i} \right ) - \alpha^n_{i-1/2} \left ( \psi  E^{n+1}_{i} + \bar{\psi} E^{n}_i - \psi E^{n+1}_{i-1} - \bar{\psi}E^{n}_{i-1} \right ) \right ] \\
- + & \left [ \zeta^n_{i+1/2} \left ( \psi E^{n+1}_{i+1} + \bar{\psi} E^{n}_{i+1} + \psi E^{n+1}_{i} + \bar{\psi} E^n_{i} \right ) - \zeta^n_{i-1/2} \left ( \psi E^{n+1}_{i} + \bar{\psi} E^n_i + \psi E^{n+1}_{i-1} + \bar{\psi}E^{n}_{i-1} \right ) \right ] \\
-- & \frac{1}{1-\psi \phi} \left [ \theta + \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) - \omega v^n_x \left ( \psi E^{n+1}_{i+1} - \psi E^{n+1}_{i-1} + \bar{\psi} E^n_{i+1}- \bar{\psi} E^n_{i-1} \right ) + \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right ) \right ] \\
+ + & \left [ \zeta^n_{i+1/2} v^n_{x,i+1/2} \left ( \psi E^{n+1}_{i+1} + \bar{\psi} E^{n}_{i+1} + \psi E^{n+1}_{i} + \bar{\psi} E^n_{i} \right ) - \zeta^n_{i-1/2} v^n_{x,i-1/2}\left ( \psi E^{n+1}_{i} + \bar{\psi} E^n_i + \psi E^{n+1}_{i-1} + \bar{\psi}E^{n}_{i-1} \right ) \right ] \\
+- & \frac{1}{1-\psi \phi} \left [ \theta + \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) + \omega v^n_x \left ( \psi E^{n+1}_{i+1} + \bar{\psi} E^n_{i+1} - \psi E^{n+1}_{i-1} - \bar{\psi} E^n_{i-1} \right ) - \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right ) \right ] \\
 \end{eqnarray}
 }}}
@@ -478 +478 @@
 and where
 
-[[latex(\zeta_{i+1/2}= \frac{\Delta t}{\Delta x}\frac{3-R_{2,i+1/2}}{2} v^n_x,{i+1/2} )]]
+[[latex(\zeta_{i+1/2}= \frac{\Delta t}{\Delta x}\frac{3-R_{2,i+1/2}}{2} )]]
 
 and 
@@ -490 +490 @@
 and
 
-[[latex(\theta = f(e^n_i) = \epsilon^n_i \frac{4 \pi}{c} B \left ( T^n_i \right ) )]]
+[[latex(\theta = \Delta t f(e^n_i) = \epsilon^n_i \frac{4 \pi}{c} B \left ( T^n_i \right ) )]]
 
 and