Changes between Version 128 and Version 129 of FluxLimitedDiffusion

Timestamp:

03/30/13 23:20:06 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -412 +412 @@
 Then if we take the semi-discretized equation for E 
 
-  [[latex(\frac{\partial E}{\partial t} = \nabla \cdot \frac{c \lambda}{\kappa_{0R}} \nabla E - \nabla \cdot \left ( \frac{3-R_2}{2} \mathbf{v} E \right ) - f \left ( e^n_i \right ) - g \left ( E, \nabla E \right ) - \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i -  \psi \phi e^{n+1}_i )]]  
+  [[latex(\frac{\partial E}{\partial t} = \nabla \cdot \frac{c \lambda}{\kappa_{0R}} \nabla E - \nabla \cdot \left ( \frac{3-R_2}{2} \mathbf{v} E \right ) - f \left ( e^n_i \right ) - g \left ( E, \nabla E \right ) - \frac{1}{\Delta t} \left ( \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i -  \psi \phi e^{n+1}_i \right ) )]]  
 
 and then plugin the solution for e^n+1^,,i,, we get
 
-  [[latex(\frac{\partial E}{\partial t} = \nabla \cdot \frac{c\lambda}{\kappa_{0R}} \nabla E -\nabla \cdot \left ( \frac{3-R_2}{2}\mathbf{v}E \right ) - f \left (e^n_i \right ) - g \left (E, \nabla E \right ) - \frac{1}{\Delta t} \left ( \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i  - \psi \phi e^n_i - \frac{\psi \phi }{1-\psi \phi} \left ( f \left ( e^n_i \right ) + g \left (E,\nabla E \right ) \right ) \right ) )]]  
+  [[latex(\frac{\partial E}{\partial t} = \nabla \cdot \frac{c\lambda}{\kappa_{0R}} \nabla E -\nabla \cdot \left ( \frac{3-R_2}{2}\mathbf{v}E \right ) - f \left (e^n_i \right ) - g \left (E, \nabla E \right ) - \frac{1}{\Delta t} \left ( \left ( \left ( \bar{\psi} - 1  \right ) \phi \right ) e^n_i  - \psi \phi e^n_i \right ) - \frac{\psi \phi }{1-\psi \phi} \left ( f \left ( e^n_i \right ) + g \left (E,\nabla E \right ) \right ) )]]  
 
 which simplifies to