Changes between Version 29 and Version 30 of FluxLimitedDiffusion

Timestamp:

03/20/13 12:37:07 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -78 +78 @@
 
 
-For static diffusion, the terms in blue with v^2^/c can be dropped and the system can be split into the usual hydro update (black), radiative source terms (green) using time centered radiation energy, and a coupled implicit solve (red) for the radiation energy density and thermal energy density (ie temperature).  If the opacity is independent of temperature and radiation energy density, then the implicit solve only involves the radiation energy density.  Otherwise some sort of sub-cycling would be required.
+For static diffusion, the terms in blue with v^2^/c can be dropped and the system can be split into the usual hydro update (black), radiative source terms (green), and a coupled implicit solve (red) for the radiation energy density and thermal energy density (ie temperature). 
 
 
@@ -105 +105 @@
  * 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.
 
-== Implicit Discretization ==
+== Implicit Equation ==
 
 For now we will assume that [[latex(\kappa_{0P})]] and [[latex(\kappa_{0R})]] are constant over the implicit update and we will treat the energy as the total internal energy ignoring kinetic and magnetic contributions.  In this case we can solve the radiation energy equations:
@@ -132 +132 @@
 
 
-=== 1D ===
+=== Implicit Discretization ===
 Which we can discretize for (1D) as
 
@@ -163 +163 @@
 [[latex(\frac{\Delta t}{\Delta x}\mathbf{F}^n_{i+1/2} = \alpha^n_{i+1/2} \left ( E^{*}_{i+1} - E^{*}_i \right ) )]]
 
+=== Time Discretization ===
 
 Now all the terms on the right hand side that are linear in E or e have been written as E^*^ or e^*^ because there are different ways to approximate E^*^ (e^*^).  For Backward Euler we have