Radiative Shock Simulation

In this problem, you set the ambient conditions and use shock jump equations to solve for initial post-shock conditions. Then, the initial post-shock conditions become your initial boundary conditions for the ODE inside the cooling region. I've been using Mathematica to solve this ODE for the pressure profile. The profiles for other important hydro quantities follow from this. The analytic form that Mathematica gives is not pretty, but when plotted it looks qualitatively correct.

For a while, I was struggling to get my profiles to look like those in Delamarter '01. I realized that the solutions for the pressure, temperature, etc. profiles in the cooling region are strongly dependent on gamma. So I made gamma a free parameter again, instead of just using 5/3. One problem is that Delamarter makes no mention of what value he used for gamma. Also, he does not give values for the initial post-shock quantities, so there is no way to calculate what he used for gamma. The best I can do is guess by looking at the plots. I think I get close to the initial post-shock values with a gamma of 1.25. The profiles look qualitatively correct, but my cooling region is about 10 cells (2.5*1016 cm) smaller than that of the Delamarter simulation.

Another issue is that my solutions are not steady on the timescales stated in Delamarter. It should be relatively steady for at least 4000 years, but my solutions are not at all.

I see four possible reasons for these discrepancies:

1) There is something wrong in AstroBEAR

2) There is something wrong with the Delamarter simulations/calculations

3) The analytic formulas from Mathematica are wrong+

4) I am still not using gamma correctly++

+Note that I solved the differential equations in Mathematica analytically and numerically…the results are the same.

++Another thing that I haven't tried yet is using two different gammas. One gamma for the cooling region, and a different gamma elsewhere.

I have not yet tried using my own numerical ODE solver, so maybe that's the next step. I'll post some equations and plots before our next group meeting.

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