wiki:u/lchamandy/2017-04-17

Version 8 (modified by Luke, 8 years ago) ( diff )

With smoothed , resolution , cm, and run time seconds dynamical times, No velocity damping, unless otherwise indicated

I) Boundary conditions on the Poisson solver

Motivation:

  • It was realized last meeting that "Multipole expansion" BCs on the Poisson solver might be more reasonable than periodic BCs.
  • Therefore I did a run that was the same as the fiducial run from last blog post but with Multipole expansion.

Setup:
Simply changed the Poisson BCs in the global.data file.

Results:

a) Periodic BCs, no velocity damping
(i) Constant ambient pressure and density (Ambp038, 5.2 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm001, 4.1 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

b) Multipole expansion BCs, no velocity damping
(i) Constant ambient pressure and density (Damp010, 5 hrs on comet compute, 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm003)
2d density 2d density and velocity

Comparison with (a) on left and (b) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

  • Case (b) becomes boxy and goes unstable a bit earlier than case (a)
  • No oscillations are present in (b), contrary to (a).
  • Outside of the star, velocity magnitudes are similar in (a) and (b).

Conclusion
Multipole expansion (ME) BCs is more physical. It averts unphysical oscillations. Therefore, we adopt ME BCs below.

II) Boundary conditions on the hydrodynamical quantities

Motivation:

  • With extrapolated BCs we obtain reflections at the boundary and inflows.
  • We want to try other BCs to avert these reflections/inflows as much as possible.

Setup:

1) Fix the boundaries to the values of , and of the initial profile
or
2) Draw a sphere with radius and fix the points outside this sphere to the values of , , and of the initial profile.

Results:

a) Extrapolated hydro BCs, Multipole expansion Poisson BCs, no velocity damping (same as (b) in Sect. I above)
(i) Constant ambient pressure and density (Damp010)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm003)
2d density 2d density and velocity

b) Fixed profile (, , ) on boundary hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp017, 9 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm004)
2d density 2d density and velocity

c) Fixed profile outside sphere (of radius cm) hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp018, 26 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm008)
2d density 2d density and velocity 2d density extended range

d) Fixed pressure on boundary with rho and veloc extrapolated hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp023, 6.6 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

e) Fixed pressure and density on boundary with veloc extrapolated hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp025, 9 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

f) Fixed pressure outside spherical region with rho and veloc extrapolated hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp024, 7.7 hrs on comet compute, 576 cores)
2d density and velocity

(ii) Isothermal hydrostatic atmosphere (pending on stampede) (Atm010)
2d density 2d density and velocity

g) Fixed profile outside sphere of radius cm instead of cm, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp026, 26.6 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

h) Fixed pressure outside sphere ( cm) with rho and veloc extrapolated hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp027, 9.6 hrs on comet compute, 576 cores)
2d density 2d density and velocity

i) Reflecting hydro BCs, Multipole expansion Poisson BCs, no velocity damping
(i) Constant ambient pressure and density (Damp028, 6.9 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

(ii) Isothermal hydrostatic atmosphere, no velocity damping (Atm011, 11 hrs on bluehive standard, 120 cores)
2d density 2d density and velocity 2d density extended 2d density and velocity extended

Comparison with (a) on left and (b) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with (b) on left and © on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with (b) on left and (d) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with (a) on left and (i) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with (b) on left and (i) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

  • Fixing the profile on the boundary (b) results in a somewhat more stable star compared with the fiducial case (a).
  • Fixing the profile outside a sphere © results in a marginally more stable star compared with case (b).
  • Using reflecting hydro BCs (i) gives almost identical results as fixing the profile at the boundary (b).

Conclusions:

  • The marginal improvement in going from case (b) to case © probably does not justify the need to artificially fix the hydrodynamical variables within the computation zone. But anyway, we consider both cases when we include damping below.
  • Fixing P on a spherical boundary while leaving other variables unconstrained may prevent inflow (Oliger+Sundstrom78, Rudy+Strikwerda80). This should be tried before we go on to longer more computationally intensive runs. Although in case (h) the star retains its spherical morphology for longer, other instabilities are driven due to inflow. It might be worth trying this case with damping.
  • Interestingly, reflecting BCs (i) are almost as good as fixing the profile at the boundaries (b). Since the former avoids the extra computation step of resetting the boundary to the initial profile every time step, reflecting hydro BCs are probably preferable to fixing the profile at the boundary.

III) Damping

Motivation:
To improve the stability we now add an artificial damping of the velocity.

Setup:
In ProblemBeforeStep, we convert from conservative to primitive mode and alter the velocity, as discussed last blog post (implementation 3).

Results:

(NOTE THAT VELOCITY VECTORS ARE SCALED 10 TIMES LARGER FOR CASES WITH DAMPING UNLESS STATED OTHERWISE)
a) Fixed profile on boundary hydro BCs, Multipole expansion Poisson BCs, no velocity damping (same as II(b) above)
(i) Constant ambient pressure and density (Damp017, 9 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm004)
2d density 2d density and velocity

b) Fixed profile on boundary hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s
(i) Constant ambient pressure and density (Damp021, 9.4 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

c) Fixed profile outside sphere hydro BCs, Multipole expansion Poisson BCs (same as II© above), no velocity damping
(i) Constant ambient pressure and density (Damp018, 26 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm008)
2d density 2d density and velocity

d) Fixed profile outside sphere hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s
(i) Constant ambient pressure and density (Damp022, 26 hrs on bluehive standard 120 cores)
2d density 2d density and velocity 2d pressure 1d density 1d pressure

(ii) Isothermal hydrostatic atmosphere (Atm009)
2d density and velocity 2d density and velocity (10x smaller arrows) 2d density and velocity (extended color bar, smaler arrows)

e) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with s

(i) Constant ambient pressure and density (Damp029, 6.9 hrs on bluehive standard 120 cores)
2d density 2d density and velocity

(ii) Isothermal hydrostatic atmosphere (Atm012, 11.5 hrs on bluehive standard, 120 cores)
2d density 2d density and velocity (10x smaller arrows) 2d density (extended color bar) 2d density and velocity (extended color bar, 10x smaller arrows)

Comparison with (a) on left and (b) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with © on left and (d) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

Comparison with (b) on left and (d) on right
(i) Constant ambient pressure and density
2d density 2d density and velocity

  • Damping preserves the morphology better and helps the star to remain stable. This is consistent with results from the last blog post with different boundary conditions.
  • Fixing the profile at the boundary actually improves stability slightly compared to fixing the profile outside a sphere. (Last plot.)

Conclusions:

  • The most successful model for keeping the star stable is III(b) above. Thus III(b) will now be treated as fiducial.
  • From past experiments, we know that stability should improve with increased resolution and larger box size. This should allow larger values of to be imployed, as the current value of is only about dynamical times, smaller than what is used by Ohlmann.
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