Changes between Version 30 and Version 31 of FluxLimitedDiffusion

Timestamp:

03/20/13 12:43:32 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -228 +228 @@
 
 === Reflecting Boundary ===
-Reflecting boundary should be fairly straightforward.  This an be achieved by setting [[latex(\alpha_g = 0)]] which zeros out any flux - and has the same effect as setting [[latex(E^{n+1}_g=E^{n+1}_i)]]
+Reflecting boundary should be fairly straightforward.  This an be achieved by setting [[latex(\alpha_g = 0)]] which zeros out any flux - and has the same effect as setting [[latex(E^{*}_g=E^{*}_i)]] or [[latex(E^{n+1}_g=E^{n+1}_i \mbox{ and } E^{n}_g=E^{n}_i)]]
 
 === Constant radiative flux ===
 To have a constant radiative flux we must have 
-[[latex(\alpha_g \left ( E^{n+1}_i-E^{n+1}_g \right ) = F_0 \frac{\Delta t}{\Delta x})]]
+[[latex(\alpha_g \left ( E^{*}_i-E^{*}_g \right ) = F_0 \frac{\Delta t}{\Delta x})]]
 
 Which we can solve for 
-[[latex(E^{n+1}_g = E^{n+1}_i - \frac{F_0 \Delta t}{\alpha_g \Delta x})]]
+[[latex(E^{*}_g = E^{*}_i - \frac{F_0 \Delta t}{\alpha_g \Delta x})]]
 
 but when we plug this into the coefficient matrix the terms with [[latex(\alpha_g)]] cancel and we just get [[latex(F_0 \frac{\Delta t}{\Delta x})]] in the source vector