Version 14 (modified by 8 years ago) ( diff ) | ,
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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
DESCRIPTION: Star expands and contracts, becoming first more diamond-shaped and then more square-shaped.
(ii) Isothermal hydrostatic atmosphere (Atm001, 4.1 hrs on bluehive standard 120 cores)
2d density
2d density and velocity
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm003)
2d density
2d density and velocity
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
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.
- Fixing P on a spherical boundary while leaving other variables unconstrained may prevent inflow (Oliger+Sundstrom78, Rudy+Strikwerda80). This was tried below (case h).
Setup:
- In ProblemBeforeStep we try two alternative BCs, in turn:
1) Fix the boundaries to the values of
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
DESCRIPTION: Star becomes square-shaped, and unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm003)
2d density
2d density and velocity
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
b) Fixed profile (
(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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm004)
2d density
2d density and velocity
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
c) Fixed profile outside sphere (of radius
(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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm008)
2d density
2d density and velocity
2d density extended range
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
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
DESCRIPTION: Ambient medium becomes unstable and instabilities propagate inward after a few dynamical times, destroying star.
(ii) Isothermal hydrostatic atmosphere (run on stampede) (Atm010)
2d density and velocity
DESCRIPTION: Very large velocities at early times at corners of grid.
g) Fixed profile outside sphere of radius
(i) Constant ambient pressure and density (Damp026, 26.6 hrs on bluehive standard 120 cores)
2d density
2d density and velocity
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
h) Fixed pressure outside sphere (
(i) Constant ambient pressure and density (Damp027, 9.6 hrs on comet compute, 576 cores)
2d density
2d density and velocity
DESCRIPTION: Ambient medium becomes unstable and instabilities propagate inward after a few dynamical times, destroying star.
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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(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
DESCRIPTION: Star preserves its shape rather well but region exterior to star begins to be unstable after a few dynamical times.
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).
- 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.
- 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.
- 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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm004)
2d density
2d density and velocity
DESCRIPTION: Star becomes unstable after about 1 dynamical time.
b) Fixed profile on boundary hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(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
DESCRIPTION: Square-shaped morphology and velocities reduced from case III(a), but still begins to be unstable after a few dynamical times.
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
DESCRIPTION: Star becomes square-shaped, starts to become unstable after a few dynamical times.
(ii) Isothermal hydrostatic atmosphere (Atm008)
2d density
2d density and velocity
DESCRIPTION: Ambient medium becomes unstable after about 1 dynamical time.
d) Fixed profile outside sphere hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(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
DESCRIPTION: Square-shaped morphology and velocities reduced from case III(a), but still begins to be unstable after a few dynamical times.
(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)
DESCRIPTION: Rather steady and preserves shape rather well at ~1 dynamical time.
e) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp029, 6.9 hrs on bluehive standard 120 cores)
2d density
2d density and velocity
DESCRIPTION: Square-shaped morphology and velocities reduced from case III(a), but still begins to be unstable after a few dynamical times.
(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)
DESCRIPTION: Preserves shape rather well, but instabilities build up in ambient medium and propagate inward after a few dynamical times.
f) Extrapolated hydro BCs, periodic Poisson BCs
(i) Constant ambient pressure and density (Damp008)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
g) Extrapolated BCs, multipole expansion Poisson BCs
(i) Constant ambient pressure and density (Damp009)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
h) Extrapolated BCs, multipole expansion Poisson BCs
(i) Constant ambient pressure and density (Damp011)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
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
Comparison with (b) on left and (e) 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.
- Reflecting BCs (e) gives almost identical results to holding profile fixed on boundaries (b). But with reflecting BCs the simulation is about 30% faster.
Conclusions:
- The most successful model for keeping the star stable is III(e) above with constant ambient pressure and density.
IV) Large box (double box size and number of cells to
Results:
a) Extrapolated hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp013)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
DESCRIPTION: Develops slightly boxy morphology.
b) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp046)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
DESCRIPTION: Develops slightly boxy morphology.
c) Reflecting hydro BCs, Multipole expansion Poisson BCs, No velocity damping
(ii) Isothermal hydrostatic atmosphere (Atm013)
2d density
2d density (extended color bar)
2d density (extended color bar) and velocity
DESCRIPTION: flow becomes complex, unstable. Code crashed after ~1 dynamical time.
Comparison with (a) on left and (b) on right
(i) Constant ambient pressure and density
2d density
2d density and velocity
- The reflecting BCs case is slightly more stable compared to the extrapolated boundaries case.
V) AMR with large box
Results:
a) Extrapolating hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp047, 27 hrs on comet compute, 576 cores) —arrows scaled as in section II without damping
2d density
2d density and velocity
DESCRIPTION: More square-shaped and a few times larger velocities than in Sect IV above.
b) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp044) —arrows scaled as in section II without damping
2d density
2d density and velocity
DESCRIPTION: More square-shaped and a few times larger velocities than in Sect IV above.
(ii) Isothermal hydrostatic atmosphere
- Did not run with AMR due to memory problem (even after increasing from 2GB/cpu to 4GB/cpu on bluehive standard)
Overall Conclusions
- Boundaries cause the start to become cubical. There is no apparent way to avoid this by changing the boundary conditions. The problem is associated with inflow that is stronger from the sides than the corners.
- For fixed grid simulations, reflecting hydro BCs or fixing the profile on the boundary or outside a sphere seems to work best, but the former is simpler and leads to faster computation times, so is the most natural to adopt.
- AMR seems to make this "boxiness" problem worse.
- Damping helps to alleviate the problem. A damping time s prevents the boxiness problem from arising in fixed grid runs, but a s does not prevent it completely. Ohlmann et al. 2017 uses a scheme whereby starts out small (1/10 of the dynamical time for 2 dynamical times) and then increases gradually until it is turned off at 5 dynamical times. Our dynamical time is a few times s.
- The hydrostatic envelope model (ii) leads to large velocities and instabilities near the corners of the grid. It is apparently not possible to avoid this by changing the boundary conditions. Therefore, it is probably best to stick with a constant ambient pressure and density model.
- The next thing to try is to try varying the damping time using the Ohlmann et al. prescription (first for a model).