Changes between Version 134 and Version 135 of FluxLimitedDiffusion

Timestamp:

03/31/13 10:26:50 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -468 +468 @@
 E^{n+1}_i-E^{n}_i = & \left [ \alpha^n_{i+1/2} \left ( \psi E^{n}_{i+1} + \bar{\psi} E^{n+1}_{i+1}- \psi E^{n+1}_{i} - \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}_{i+1} + \bar{\psi} E^{n+1}_{i+1} + \psi E^{n+1}_{i} + \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 [ \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 ] )]]   
-
+- & \frac{1}{1-\psi \phi} \left [ \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 ] \\
+\end{eqnarray}
+}}}
 
 where the diffusion coefficient is given by