Set the following scales in physics.data:

lscale	3.08 e+18 cm
rscale	2.02 e-16 g/cm3
tempscale	1 K

From that initialized an ambient object with the following density and pressure,

ambient%rho=2.03d-16/rscale
ambient%pressure=(rhoOut/rscale)*(tempOut/tempscale)

Have my grid running from, gxbounds= -.0068 -.0068 0 .0068 .0068

I ran the sim to frame 0 to get the timescale from scales.data.

I used this to get the tsim=tdiff in computational units,

tsim=2.074e+6s/!338402526430554s = 6.13e-9

Next, I calculated the energy injection rate using the luminosity of a FHSC:

L=3.9e+29 erg s^-1
Lscale=Pscale*(lscale)³/timescale=1.46*10³³
L(cu)=2.67 e-4

Next came scaling the opacities.

The code takes specific opacity (this is in cm²/g), and then asks whether it should be constant, or multiplied by density (or temperature) to some power. I set it to be a power law scaling.

tpow=0
dpow=1

so that,

opacity=kappa*rho

I scaled the planck and rosseland opacities into computational units by:

kappa_r=0.23*mscale/(lscale)²=144.07
kappa_p=.4*mscale/(lscale)²=250.56

Radiation was set to 'diffusion and energy exchange only', rad limiter was set to 'diffusion limit'.

This all seems right to me, so then here are the results.

Tables of Results

In all of the runs, the light crossing time from center of box to edge ~ 8 days. All had an ideal EOS (which says what about heating and cooling).

Run	Luminosity (erg/s)	Kappa R (cm2/g)	Limiter	mean free path (box radii)	Egas/Erad	resolution	tdiff (days)	tcouple (days)	tsc (years) from center to edge
1	1038	.23	Diffusive	1	1,000	1282	24	8	33,000
2	1054	.23	Diffusive	1	1,000	1282	24	8	33,000
3	1029	.23	Diffusive	1	1,000	1282	24	8	33,000
4	1038	.23	Dynamic	1	1,000	1282	?	?	33,000
5	1038	2.3	Diffusive	1/10	1,000	1282	48	.8	33,000
6	1038	.23	Diffusive	1	1,000	642	24	8	33,000
7	1038	.23	Diffusive	1	100	1282	2.4	.8	33,000
8	1038	.23	Diffusive	1	1	1282	.0024	.008	33,000
9	1038	.23	Diffusive	1	.01	1282	.000024	.00008	33,000
10	1038	.23	Diffusive	1	.001	1282	etc	etc	33,000

Changing the luminosity

Run	Temps	Energies	Rlimiter	Final Density
1
2		Erad​
3		Erad​

Calculating the limitor dynamically

1
4

Decreasing the mean free path

1
5

Decreasing resolution

1
6

Decreasing Egas/Erad

1
7
8		Erad​
9				Rho remained constant
10				Rho remained constant

Description of Results

Run 1

de/dt=7.73246e+21

I calculated the diffusion time assuming the scale-height was = box radius (which also equals the mean free path). Because of this, I thought I was in the optically thick limit everywhere in my box, so chose the flux limiter to be constant… =1/3 in the data file. From this, I calculate the diffusion time to be 24 days. Is this a good estimate?

A diffusion wave is the time is take a signal to spread out over some length scale. Imagine a delta source spreading out. When its width equals its half max, is roughly a diffusion time.

Here is Erad over time:

Why do the wings leave the grid faster than the speed of light (i.e. before even frame 1)?

This has to do with the fact I am not 'limiting' the diffusion through the limiter, when I should be doing that. Instead, I am using a constant lambda, which I thought at the time might be appropriate. However, as this plot of R shows, that is not the case:

In some regions, the limiter should be smaller than 3, so as to limit the diffusion wave in optically thin regions — so that it is below the speed of light. Because that is not happening, I am getting superluminal signal. (This should be fixed by tracking lambda dynamically through the grid).

Here is a movie​ of R_limiter.

And an image of the inverse scale height:

Since, the scale height is not the same as the mean free path in actuality, getting unphysical diffusion speeds on the wings. However, given this does not represent a diffusion time, not sure it effects my prediction for a diffusion time.

Here is a movie of the temperatures over time:

Here is the density at final time:

Run 2

de/dt=7e+5

Here is Erad over time:

In this case, it seems the time it takes to diffuse has changed? Hard to tell. Wouldn't expect that to be, given the diffusion time doesn't depend on Estar.

Here is R:

Here is a movie​ of R_limiter.

Here is a movie of the temperatures over time:

Here is the density at final time:

Run 3

Same de/dt but now increasing lambda by factor of 10 (this decreases mean free path by 10x, and thus increases tdiff by 10x).

Here is Erad over time:

Here is R:

Here is a movie​ of R_limiter.

Here is a movie of the temperatures over time:

Here is the density at final time:

Run 4

Run 1 at lower resolution

Run 5

Run 1 with dynamic lambda

Run 6

Run 3 with dynamic lambda

Run 7

Run 1 with lower density (do we see the temperature /coupling change ?)