Changes between Version 65 and Version 66 of FluxLimitedDiffusion

Timestamp:

03/26/13 15:33:39 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -137 +137 @@
 [[latex(R_{2,i+1/2} = \lambda_{i+1/2}+\lambda_{i+1/2}^2 R_{i+1/2}^2)]]
 and 
-[[latex(R_{i+1/2} = \frac{\left | E^n_{i+1}-E^n_{i} \right | }{2 \kappa_{i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]
+[[latex(R_{i+1/2} = \frac{\left | E^n_{i+1}-E^n_{i} \right | }{2 \kappa_{0R,i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]
 
 and 
-[[latex(\kappa_{i+1/2} = \frac{\kappa^n_{i}+\kappa^n_{i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2} - \frac{1}{R_{i+1/2}} \right ) )]]
+[[latex(\kappa_{0R,i+1/2} = \frac{\kappa^n_{0R,i}+\kappa^n_{0R,i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2} - \frac{1}{R_{i+1/2}} \right ) )]]
 
 and
@@ -147 +147 @@
 
 and
-[[latex(R_{i} = \frac{\left | E^n_{i+1}-E^n_{i-1} \right | }{2 \kappa_{i} E^n_{i}})]]
+[[latex(R_{i} = \frac{\left | E^n_{i+1}-E^n_{i-1} \right | }{2 \kappa_{0R,i} E^n_{i}})]]
 
 [[CollapsibleEnd()]]
@@ -195 +195 @@
 where the diffusion coefficient is given by 
 
-[[latex(\alpha_{i+1/2}=\frac{\Delta t}{\Delta x^2}  \frac{c \lambda_{i+1/2}}{\kappa_{i+1/2}} \mbox{ where } \kappa_{i+1/2} = \frac{\kappa^n_{i}+\kappa^n_{i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2} - \frac{1}{R_{i+1/2}} \right ) )]]
+[[latex(\alpha_{i+1/2}=\frac{\Delta t}{\Delta x^2}  \frac{c \lambda_{i+1/2}}{\kappa_{0R,i+1/2}} \mbox{ where } \kappa_{0R,i+1/2} = \frac{\kappa^n_{0R,i}+\kappa^n_{0R,i+1}}{2} \mbox{ and } \lambda_{i+1/2} = \frac{1}{R_{i+1/2}} \left ( \coth R_{i+1/2} - \frac{1}{R_{i+1/2}} \right ) )]]
 and where
-[[latex(R_{i+1/2} = \frac{\left | E^n_{i+1}-E^n_{i} \right | }{2 \kappa_{i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]
+[[latex(R_{i+1/2} = \frac{\left | E^n_{i+1}-E^n_{i} \right | }{2 \kappa_{0R,i+1/2} \left ( E^n_i+E^n_{i+1} \right )})]]