Changes between Version 91 and Version 92 of FluxLimitedDiffusion

Timestamp:

03/27/13 23:24:57 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -499 +499 @@
 
 Now since the second equation has no spatial dependence, we can solve it for 
-   [[latex(\color{purple}{e^{n+1}_i = \frac{1}{ 1 +\psi \phi^n_i}\left \{ \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 \right \}} )]]   
+   [[latex(\color{purple}{e^{n+1}_i = \frac{1}{ 1 +\psi \phi^n_i}\left \{ \left ( \psi \epsilon^n_i \right )E^{n+1}_i - \left ( \psi \omega_i v_{x,i} \right ) E^{n+1}_{i+1} + \left ( \psi \omega_i v_{x,i} \right ) E^{n+1}_{i-1} + \left ( 1 - \bar{\psi}\phi^n_i \right ) e^n_i + \left ( \bar{\psi} \epsilon^n_i \right ) E^n_i-\theta^i_n - \bar{\psi} \omega_i v_{x,i}  \left ( E^{n}_{i+1}- E^{n}_{i-1} \right ) \right \}} )]]   
 
 and plug the result into the first equation to get a matrix equation involving only one variable.