Changes between Version 53 and Version 54 of FluxLimitedDiffusion

Timestamp:

03/24/13 14:25:23 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -110 +110 @@
  * Do ER,,0,, --- Terms with grad E can be done without ghosting since EH did not change E.  The del dot vE term needs time centered face centered velocities which can be stored during the hydro update.
 
-[[CollapsibleStart(Implicit Equation)]]
+[[CollapsibleStart(Explcit Update)]]
+The extra terms in the explicit update due to radiation energy are as follows:
+
+ [[latex(\frac{\partial }{\partial t} \left ( \rho \mathbf{v} \right ) =-\lambda \nabla E)]]   
+ [[latex(\frac{\partial e}{\partial t}  = \lambda \left ( 2 \frac{\kappa_{0P}}{\kappa_{0R}}-1 \right ) \mathbf{v} \cdot \nabla E )]]  
+ [[latex(\frac{\partial E}{\partial t}  = -\lambda \left(2\frac{\kappa_{0P}}{\kappa_{0R}}-1 \right )\mathbf{v}\cdot \nabla E -\nabla \cdot \left ( \frac{3-R_2}{2}\mathbf{v}E \right ) )]]  
+
+These can be discretized as follows:
+
+ [[latex(p^n+1_i=p^n_i - \frac{1}{2}\frac{\Delta t}{\Delta x} \lambda_{i} (E^n_{i+1}-E^n_{i-1})]]
+
+ [[latex(e^n+1_i=e^n_i + \frac{1}{2}\frac{\Delta t}{\Delta x} \lambda_i \left ( 2 \frac{\kappa^n_i_{0P}}{\kappa^n_i_{0R}}-1 \right ) \left [ v_x^n_i \left (E^n_{i+1}-E^n_{i-1} \right ) \right ] )]]  
+
+ [[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_x^n_i \left (E^n_{i+1}-E^n_{i-1} \right ) \right ] + \left ( F_{i+1/2}-F_{i-1/2} \right ) \right ])]]  
+
+
+[[CollapsibleStart(Implicit Update)]]
 == Implicit Equation ==