Changes between Version 8 and Version 9 of FluxLimitedDiffusion

Timestamp:

03/18/13 16:01:30 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -115 +115 @@
 
 ||  [[latex(E^n_i+\frac{4\pi \epsilon^n_i}{c}B \left (T^n_i \right ) )]]
+
+
+What about boundary conditions?
+
+At coarse fine boundaries, we can use time interpolated energy fields and opacities.
+== At physical boundaries we can have the following ==
+
+=== Open boundaries ===
+We would like the radiation to leave at the free streaming limit.  So 
+[[latex(\frac{c \lambda}{\kappa_{0R}} \nabla E = \mathbf{F} = cE\mathbf{n} = \frac{c \lambda_g}{\kappa_g}\frac{ \left ( E-E_g \right ) }{\Delta x})]]
+
+
+Clearly if we set [[latex(E_g = 0)]] and [[latex(\lambda_g =\kappa_g \Delta x)]] we should get the correct flux.
+
+This corresponds to an
+[[latex(\alpha = c \frac{\Delta t}{\Delta x})]]
+
+So we would just modify [[latex(\alpha)]] and zero out the matrix coefficient to the ghost zone
+
+== Thermally emitting boundary ==
+
+Another possible boundary condition would be to have the edge of the grid be adjacent to some  thermal emitter.  This corresponds to setting the radiation energy density in the ghost zones to the Planck function.
+
+[[latex(E_g = \frac{4 \pi}{c} B(T_g))]] however, we still need an opacity which could be defined from the fluid properties of the ghost region...  This would essentially be a thermally emitting boundary with the temperature, density, opacity, etc... derived from the hydro boundary type.  If the boundary type was extrapolating, and the density and temperature uniform, one could have a constant thermal energy spectrum...  However we would need to either specify the opacity and temperature of the ghost zone - or the various fluid properties needed to reconstruct the opacity and temperature of the ghost zone - or make an extra call to set physicalBC - since this may happen in between a hydro step and a physical boundary update.
+
+== 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)]]
+
+== Constant radiative flux ==
+Having a contant radiative flux