Changes between Version 125 and Version 126 of FluxLimitedDiffusion

Timestamp:

03/30/13 23:06:04 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -405 +405 @@
 and then discretized as 
 
-  [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x}  \left ( f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i +  \psi \phi e^{n+1}_i )]]
+  [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x}  \left ( f \left ( e^n_i \right ) + g \left (E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i +  \psi \phi e^{n+1}_i )]]
 
 which can be solved for 
-[[latex(e^{n+1}_i = \frac{1}{1 - \psi \phi} \left ( \left ( \bar{\psi} - 1 \right ) \phi e^n_i + f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) )]]
+[[latex(e^{n+1}_i = e^{n}_i + \frac{1}{1 - \psi \phi} \left ( f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) )]]
 
 Then if we take the semi-discretized equation for E