| 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 | |
| 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). |