Changes between Version 13 and Version 14 of u/lchamandy/2017-04-17


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Timestamp:
04/17/17 15:55:34 (8 years ago)
Author:
Luke
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  • u/lchamandy/2017-04-17

    v13 v14  
    6262- We want to try other BCs to avert these reflections/inflows as much as possible.
    6363
     64- Fixing P on a spherical boundary while leaving other variables unconstrained may prevent inflow (Oliger+Sundstrom78, Rudy+Strikwerda80). This was tried below (case h).
    6465__Setup__:\\
    6566- In ProblemBeforeStep we try two alternative BCs, in turn:\\
     
    130131DESCRIPTION: Ambient medium becomes unstable and instabilities propagate inward after a few dynamical times, destroying star.
    131132
    132 (ii) Isothermal hydrostatic atmosphere (pending on stampede) (Atm010)\\
     133(ii) Isothermal hydrostatic atmosphere (run on stampede) (Atm010)\\
    133134[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Atm010/rho2dv1e6_Atm010.gif 2d density and velocity]\\
    134135DESCRIPTION: Very large velocities at early times at corners of grid.
     
    188189- Fixing the profile outside a sphere (c) results in a marginally more stable star compared with case (b).
    189190
     191- Although in case (h) the star retains its spherical morphology for longer, other instabilities are driven due to inflow.
     192It might be worth trying this case with damping.
     193
    190194- Using reflecting hydro BCs (i) gives almost identical results as fixing the profile at the boundary (b).
    191195
     
    193197- The marginal improvement in going from case (b) to case (c) 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.
    194198
    195 - 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.
    196199
    197200- 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.
     
    273276DESCRIPTION: Preserves shape rather well, but instabilities build up in ambient medium and propagate inward after a few dynamical times.
    274277
     278'''f) Extrapolated hydro BCs, periodic Poisson BCs $\tau=10^4$ s'''\\
     279(i) Constant ambient pressure and density (Damp008)\\
     280[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp008/rho2d_Damp008.gif 2d density]
     281[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp008/vel2d_Damp008.gif 2d density and velocity]
     282[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp008/P2d_Damp008.gif 2d pressure]
     283[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp008/rho1d_Damp008.gif 1d density]
     284[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp008/P1d_Damp008.gif 1d pressure]\\
     285
     286'''g) Extrapolated BCs, multipole expansion Poisson BCs $\tau=10^4$ s'''\\
     287(i) Constant ambient pressure and density (Damp009)\\
     288[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp009/rho2ds_Damp009.gif 2d density]
     289[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp009/rho2d_Damp009.gif 2d density and velocity]
     290[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp009/P2d_Damp009.gif 2d pressure]
     291[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp009/rho1d_Damp009.gif 1d density]
     292[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp009/P1d_Damp009.gif 1d pressure]\\
     293
     294'''h) Extrapolated BCs, multipole expansion Poisson BCs $\tau=10^5$ s'''\\
     295(i) Constant ambient pressure and density (Damp011)\\
     296[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp011/rho2ds_Damp011.gif 2d density]
     297[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp011/rho2d_Damp011.gif 2d density and velocity]
     298[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp011/P2d_Damp011.gif 2d pressure]
     299[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp011/rho1d_Damp011.gif 1d density]
     300[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp011/P1d_Damp011.gif 1d pressure]\\
     301
     302
    275303'''Comparison with (a) on left and (b) on right'''\\
    276304(i) Constant ambient pressure and density\\
     
    303331
    304332'''IV) Large box (double box size and number of cells to $512^3$, so same physical resolution same)'''\\
    305 
    306 __Motivation__:\\
    307 
    308 __Setup__:\\
    309333
    310334__Results__:\\
     
    343367'''V) AMR with large box'''\\
    344368
    345 __Motivation__:\\
    346 
    347 __Setup__:\\
    348 
    349369__Results__:\\
    350370
     
    363383(ii) Isothermal hydrostatic atmosphere\\
    364384- Did not run with AMR due to memory problem (even after increasing from 2GB/cpu to 4GB/cpu on bluehive standard)
     385
     386'''__Overall Conclusions__'''
     387
     388- 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.
     389
     390- 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.
     391
     392- AMR seems to make this "boxiness" problem worse.
     393
     394- Damping helps to alleviate the problem. A damping time $\tau=10^4$s prevents the boxiness problem from arising in fixed grid runs, but a $\tau=10^5$s does not prevent it completely. Ohlmann et al. 2017 uses a scheme whereby $\tau$ 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 $10^5$s.
     395
     396- 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.
     397
     398- The next thing to try is to try varying the damping time using the Ohlmann et al. prescription (first for a $256^3$ model).