update on RGB

The past few weeks I've been trying to make progress on obtaining a stable giant. Details are available ​here but a summary is presented below.

I) Boundary conditions

  • I changed the Poisson BCs from (a) periodic to (b) multipole expansion and performed some tests. This prevents the star from oscillating. It is worth noting that Ohlmann et al. 2017 used periodic BCs and obtained oscillations.

Comparison with (a-periodic) on left and (b-multipole expansion) on right
​2d density ​2d density and velocity

  • Note that without periodic gravity, inflows from the centres of the boundary walls tend to produce "boxiness" of the star. In the hope of reducing this boxiness, I tried several variations on the hydro BCs. In the end, none of these efforts resulted in a large improvement and it seems that simply putting reflecting hydro BCs works as well or better than anything (slightly better than extrapolating, at least for a fixed grid).

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

II) Damping

  • I implemented velocity damping (see also last blog post), with a constant damping time s (about dynamical times) or, in a few cases, s. The latter value can prevent the boxiness, even in a small box with only moderate resolution. I performed some tests with larger boxes and found the results to be basically consistent with those of the smaller box runs.

Extrapolated BCs, multipole expansion Poisson BCs s
​2d density ​2d density and velocity ​2d pressure ​1d density ​1d pressure

Extrapolated BCs, multipole expansion Poisson BCs s
​2d density ​2d density and velocity ​2d pressure ​1d density ​1d pressure

Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s
​2d density ​2d density and velocity

Comparison with (a-large box extrapolating) on left and (b-large box reflecting) on right, s
(i) Constant ambient pressure and density
​2d density ​2d density and velocity

III) Hydrostatic atmosphere

  • With a hydrostatic atmosphere (rather than a constant pressure and density ambient medium), we might expect it to be easier to obtain a steady state. Long story short, the low densities and sharp gradients at the boundaries lead to large spurious velocities that tend to increase the computation time (or cause the code to crash).

Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s
​2d density ​2d density and velocity ​2d density (extended color bar) ​2d density and velocity (extended color bar)

IV) AMR

  • I performed two AMR runs (with s velocity damping and either extrapolated hydro BCs or reflecting hydro BCs).
  • Inside of cm, the refinement level was forced by hand to be equal to the highest level.

a) Extrapolating hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s, , maxlevel=4
(i) Constant ambient pressure and density (Damp047, 27 hrs on comet compute, 576 cores)
​2d density ​2d density and velocity

b) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s, , maxlevel=4
(NOTE THAT THIS HAS ONLY RUN FOR 2/3 OF THE TIME AS (a))
(i) Constant ambient pressure and density (Damp044)
​2d density ​2d density and velocity

Conclusions

  • "Boxiness" of the star owing to inflows from the centres of the boundaries has been a problem both because a cubical star is unphysical and because it eventually leads to instabilities at the star "corners."
  • Small improvements can be made by varying the BCs. For Poisson, we may choose periodic or multipole expansion. For hydro, either extrapolating or reflecting.
  • More complicated hydro BCs (e.g. fixing the ghost zones or the region exterior to some pre-defined sphere to be equal to the initial ambient values) probably do not generate enough improvement (sometimes not any) to be worth the extra computational cost.
  • From past blog posts, we know that reducing the ambient pressure by a factor of a few may also help to reduce the boxiness (though the pressure scale-height at the surface will be smaller, thus not as resolved).
  • What works best against boxiness and instability at the surface is velocity damping, which has now been implemented successfully. Using s keeps the star completely stable (at least for a uniform fixed grid), while s leads to a significant reduction in boxiness.
  • The boxiness/inflow problem becomes worse with AMR, but the star remains remarkably stable after a few dynamical times with s damping.
  • Using a hydrostatic envelope (instead of a constant density-pressure ambient medium) reduces the boxiness, but causes instabilities to develop at the corners of the grid, which then propagate inward. The code tends to crash, and I could not get it to run at all in AMR.

Next steps

  • Given the above conclusions, it is probably best to stick with a constant density and pressure ambient medium.
  • The logical next step is to try the prescription outlined in Ohlmann et al. 2017 which starts with a small and gradually ramps it up to .
  • This should be done concurrently for 1) a fixed uniform grid simulation, 2) AMR simulation.

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