Version 1 (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
2d density
2d density and velocity
2d pressure
1d density
1d pressure
b) Multipole expansion BCs
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Comparison with (a) on left and (b) on right
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:
- 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 (same as (b) in Sect. I above)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
b) Fixed profile on boundary hyrdro BCs, Multipole expansion Poisson BCs
2d density
2d density and velocity
2d pressure
1d density
1d pressure
c) Fixed profile outside sphere hydro BCs, Multipole expansion Poisson BCs
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Comparison with (a) on left and (b) on right
2d density
2d density and velocity
Comparison with (b) on left and © on right
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).
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.
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)
a) Fixed profile on boundary hydro BCs, Multipole expansion Poisson BCs (same as II(b) above)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
b) Fixed profile on boundary hyrdro BCs, Multipole expansion Poisson BCs, Velocity damping with
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(b) above)
2d density
2d density and velocity
2d pressure
1d density
1d pressure
d) Fixed profile outside sphere hyrdro BCs, Multipole expansion Poisson BCs, Velocity damping with
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Comparison with (a) on left and (b) on right
2d density
2d density and velocity
Comparison with © on left and (d) on right
2d density
2d density and velocity
Comparison with (b) on left and (d) on right
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.
- The hydro BCs used do not completely prevent inflow. It is a possible that 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.