Changes between Version 4 and Version 5 of u/lchamandy/2017-04-17


Ignore:
Timestamp:
04/07/17 19:22:31 (8 years ago)
Author:
Luke
Comment:

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  • u/lchamandy/2017-04-17

    v4 v5  
    122122
    123123'''g) Fixed profile outside sphere of radius $4\times10^{12}$ cm instead of $5\times10^{12}$ cm, Multipole expansion Poisson BCs'''\\
    124 (i) Constant ambient pressure and density (pending on bluehive)\\
    125 [http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp024/rho2d_Damp026.gif 2d density]
    126 [http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp024/rho2dv1e6_Damp026.gif 2d density and velocity]\\
     124(i) Constant ambient pressure and density\\
     125[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp026/rho2d_Damp026.gif 2d density]
     126[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp026/rho2dv1e6_Damp026.gif 2d density and velocity]\\
    127127
    128128'''h) Fixed pressure outside sphere ($r=4\times10^{12}$ cm) with rho and veloc extrapolated hydro BCs, Multipole expansion Poisson BCs'''\\
    129 (i) Constant ambient pressure and density (pending on comet)\\
    130 [http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp024/rho2d_Damp027.gif 2d density]
    131 [http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp024/rho2dv1e6_Damp027.gif 2d density and velocity]\\
     129(i) Constant ambient pressure and density\\
     130[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp027/rho2d_Damp027.gif 2d density]
     131[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp027/rho2dv1e6_Damp027.gif 2d density and velocity]\\
     132
     133'''i) Reflecting hydro BCs, Multipole expansion Poisson BCs'''\\
     134(i) Constant ambient pressure and density\\
     135[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp028/rho2ds_Damp028.gif 2d density]
     136[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Damp028/rho2dv1e6_Damp028.gif 2d density and velocity]\\
     137
     138(ii) Isothermal hydrostatic atmosphere (running on bluehive)\\
     139[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Atm011/rho2d_Atm011.gif 2d density]
     140[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Atm011/rho2dv1e6_Atm011.gif 2d density and velocity]\\
    132141
    133142'''Comparison with (a) on left and (b) on right'''\\
    … …  
    146155[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/rho2dv1e6_fix_fixP.gif 2d density and velocity]
    147156
     157'''Comparison with (a) on left and (i) on right'''\\
     158(i) Constant ambient pressure and density\\
     159[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/rho2d_extrap_reflec.gif 2d density]
     160[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/rho2dv1e6_extrap_reflec.gif 2d density and velocity]
     161
     162'''Comparison with (b) on left and (i) on right'''\\
     163(i) Constant ambient pressure and density\\
     164[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/rho2d_fix_reflec.gif 2d density]
     165[http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/rho2dv1e6_fix_reflec.gif 2d density and velocity]
     166
    148167- Fixing the profile on the boundary (b) results in a somewhat more stable star compared with the fiducial case (a).
    149168
    150169- Fixing the profile outside a sphere (c) results in a marginally more stable star compared with case (b).
    151170
     171- Using reflecting hydro BCs (i) gives almost identical results as fixing the profile at the boundary (b).
     172
    152173__Conclusions__:\\
    153 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.
     174- 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.
     175
     176- 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.
     177
     178- 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.
    154179
    155180'''III) Damping '''\\
    … …  
    231256
    232257- From past experiments, we know that stability should improve with increased resolution and larger box size. This should allow larger values of $\tau$ to be imployed, as the current value of $1\times10^5$ is only about $0.2$ dynamical times, smaller than what is used by Ohlmann.
    233 
    234 - 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.