Changes between Version 60 and Version 61 of FluxLimitedDiffusion

Timestamp:

03/24/13 21:14:29 (13 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -130 +130 @@
  [[latex(E^{n+1}_i=E^n_i - \frac{\Delta t}{\Delta x} \left ( \frac{\lambda_i}{2} \left ( 2 \frac{\kappa^n_{i,0P}}{\kappa^n_{i,0R}}-1 \right ) \left ( v^n_i \left ( E^n_{i+1}-E^n_{i-1} \right ) \right ) + \left ( F_{i+1/2}-F_{i-1/2} \right ) \right ))]]  
 
+where
+[[latex(F_{i+1/2}=\frac{3-R_{2,i+1/2}}{8} \left(v_{i}^n+v_{i+1}^n \right ) \left ( E^n_i+E^n_{i+1/2} \right ) )]]
+
+where
+
+[[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 )})]]
+
+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 ) )]]
+
+and
+
+[[latex(\lambda_{i} = \frac{1}{R_{i}} \left ( \coth R_{i} - \frac{1}{R_{i}} \right ) )]]
+
+and
+[[latex(R_{i} = \frac{\left | E^n_{i+1}-E^n_{i-1} \right | }{4 \kappa_{i} \left ( E^n_{i-1}+E^n_{i+1} \right )})]]
+
 [[CollapsibleEnd()]]