Introduction
The last blog post I was struggling to avoid a cubical ("boxy") and thus unstable star. This boxiness is worse with AMR but reduces with damping. However, we cannot keep damping turned on indefinitely. I had found that changing the BCs can make a difference. It occurred to me that using periodic BCs may avoid this problem. Periodic BCs were used by Ohlmann+17. I experimented again with different BCs in Sections I and II.

In Section II below I vary the value of the damping time scale \tau according to the prescription of Ohlmann+17, using the free-fall time 3\times10^5 s as the dynamical timescale t_\mathrm{dyn}, rather than the more conservative sound-crossing time of 7.5\times10^5. Here \tau is ramped up to \infty over 5t_\mathrm{dyn}, and then left undamped for another 5t_\mathrm{dyn}. In Section III I try a run that includes AMR and the Ohlmann damping prescription (still running).

Results

• For the small-box simulations without AMR of Section II below, the periodic/periodic hydro/Poisson BCs seem to help to keep the star spherical,

though they increase the computation time by a factor of a few compared to extrapolating/multipole expansion BCs.

• For AMR and a twice larger box, the BCs seem to matter much less (see comparison of Ib and If below).

• It donned on me that maybe the ambient pressure is just too high at 10^7 dyne/cm^2, and that this leads to boxiness. This value had led to a more stable star than 10^6 dyne/cm^2 in the small-box low res uniform grid sims. But with AMR we can still resolve the outer scale height if the ambient pressure is 10^6.

• So I did some runs with 10^6 dyne/cm^2, and the results were encouraging. Not only is the star more spherical, but the computation time is typically reduced by a factor of a few.

• The star is still not perfectly spherical nor perfectly stable for the 10^6 dyne/cm^2 runs below, but clearly reducing the ambient pressure is the correct thing to do.

Next steps

• Run III(a) is ongoing. In the meantime, it will be worth doing the same run but with Extrapolating/multipole expansion BCs, which should be faster. If the results are similar, I will stick with the Extrapolating/multipole expansion, which are probably more physical than periodic/periodic and reduce the computation time.

• Simultaneously I will try the same run but with ambient pressure reduced to 10^5 dyne/cm^2 and 3\times10^5 dyne/cm^2 to see if further improvements can be made. Clearly the pressure must be as low as possibly while still adequately resolving the scale height at the surface.

• Then it would be worth increasing the box size and resolution to be more comparable with those of Ohlmann+17. At this point we would have to make a final choice for the ambient pressure and dynamical time scale.

• After this, if everything looks good, we need to test the stability of the star as it translates along the grid. Finally we can introduce the secondary (point particle).

I) Damping with AMR
a) Reflecting hydro BCs, Multipole expansion Poisson BCs, \tau=10^5 s, ambient P=10^7 dyne/cm^2 (Damp044)
​2d density ​2d density and velocity

b) Extrapolating hydro BCs, Multipole expansion Poisson BCs, \tau=10^5 s, ambient P=10^7 dyne/cm^2 (Damp047 27 hrs on comet compute 576 cores)
​2d density ​2d density and velocity

c) Extrapolating hydro BCs, Multipole expansion Poisson BCs, \tau=10^4 s, ambient P=10^7 dyne/cm^2 (Damp049)
​2d density ​2d density and velocity

d) Extrapolating hydro BCs, Multipole expansion Poisson BCs, \tau=3\times10^4 s, ambient P=10^7 dyne/cm^2 (Damp050 run on comet)
​2d density ​2d density and velocity

e) Extrapolating hydro BCs, Multipole expansion Poisson BCs, \tau=1\times10^5 s, ambient P=10^6 dyne/cm^2 (Damp058 run on comet)
​2d density ​2d density and velocity

f) Periodic hydro BCs, Periodic Poisson BCs, \tau=1\times10^5 s, ambient P=10^7 dyne/cm^2 (Damp057 22 hrs on stampede normal 512 cores)
​2d density ​2d density and velocity

Comparison with (a) on left and (b) on right
​2d density ​2d density and velocity

Comparison with (b) on left and (f) on right
​2d density ​2d density and velocity

II) Damping with evolving tau

• Damping prescription as in Ohlmann+17, using t_\mathrm{dyn}=3\times10^5s (about equal to the freefall time, while the sound-crossing time is about 7.5\times10^5s).

a) Reflecting hydro BCs, Multipole expansion Poisson BCs, ambient P=10^7 dyne/cm^2 (Damp051)
​2d density ​2d density and velocity

b) Extrapolating hydro BCs, Multipole expansion Poisson BCs, ambient P=10^7 dyne/cm^2 (Damp052 9 hrs on bluehive standard 120 cores)
​2d density ​2d density and velocity

c) Extrapolating hydro BCs, Periodic Poisson BCs, ambient P=10^7 dyne/cm^2 (Damp053 8 hrs on bluehive standard 120 cores)
​2d density ​2d density and velocity

d) Periodic hydro BCs, Periodic Poisson BCs, ambient P=10^7 dyne/cm^2 (Damp054 33 hrs on bluehive standard 120 cores)
​2d density ​2d density and velocity

e) Extrapolating hydro BCs, Multipole expansion Poisson BCs, ambient P=10^6 dyne/cm^2 (Damp055 4 hrs on bluehive standard 120 cores)
​2d density ​2d density and velocity

f) Periodic hydro BCs, Periodic Poisson BCs, ambient P=10^6 dyne/cm^2 (Damp056 10 hrs on bluehive standard 120 cores)
​2d density ​2d density and velocity

III) Damping with AMR and evolving tau
a) Periodic hydro BCs, Periodic Poisson BCs, ambient P=10^6 dyne/cm^2 (Damp059 bluehive standard 120 cores up to 33 then bluestreak 8192 cores)
​2d density ​2d density and velocity


UPDATE, May 9, 2017

• Run III(a) above is almost but not quite complete now (120 of 150 frames). It is running on bluestreak
  

III) Damping with AMR and evolving tau
a) Periodic hydro BCs, Periodic Poisson BCs, ambient P=10^6 dyne/cm^2
(Damp059 bluehive standard 120 cores up to 33 then bluestreak 8192 cores, 2 cpus/task up to t=2.4\times10^5 s=8t_\mathrm{dyn})
(L=2\times10^{13} cm, 64^3, 4 levels AMR)
​2d density

b) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient P=10^6 dyne/cm^2
(L=2\times10^{13} cm, 64^3, 4 levels AMR)
(Damp060 stampede normal, about 2 days with 1024 cores, 1 cpu/task for half and then 512 cores, 1 cpu/task for half)
​2d density

c) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient P=10^6 dyne/cm^2
(L=4\times10^{13} cm, 64^3, 5 levels AMR)
(Damp062 Bluehive standard 120 cores up to frame 7 and then about 2 days on comet compute 864 cores, 2 cpus/task up to frame 150 )
​2d density

Discussion

• Ohlmann+17 also tried an adaptive cubic grid and found results that were almost identical to results using their HEALPix grid. But their simulations employed a moving mesh "with an adaptive refinement ensuring similar cell masses."

Next Steps?

• Increase box size further to L=8\times10^{13} cm (64^3 with 6 levels of AMR or 128^3 with 5 levels of AMR?).
• Increase max resolution by a factor of two.

Computing Issues

• Current runs take about two days on XSEDE/comet (or a little less on stampede) with the max number of cores, plus a few days in the queue, so say 1 week per run. Each frame produces a chombo file of about 20 GB.

• Is it better to use 64^3 and 5 levels AMR or 128^3 and 4 levels of AMR?

• Would I gain much by forcing only the center and surface of the star to have max refinement instead of the whole star?

• How does the result depend on choice of machine used, e.g. bluestreak vs stampede?

• When running jobs that need more than the default memory, is it necessary to run with half the cores?

Upcoming Conferences
​The Physics of Evolved Stars: The Role of Binarity
Nice, France, July 10-13, 2017
Accepted for a poster. Possibility of sharing a talk slot.

​The Impact of Binaries on Stellar Evolution
Garching, Germany, July 3-7, 2017
Accepted for a poster.