Version 12 (modified by 7 years ago) ( diff ) | ,
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Bondi Accretion
3/18/2018 (
case)Am working on a 3D simulation of Bondi Flow onto a central sink particle and studying the accretion properties using the Krumholz accretion algorithm.
The setup has the following parameters (in computational units):
Lx=Ly=Lz | 20 |
MaxLevel (AMR) | 2 |
Mx=My=Mz | 64 |
Effective resolution (dx) | .15625 |
Sink dx = 4dx | .625 |
From Bondi (1952) we have the following quantities (in order: Bondi radius, accretion rate, sonic radius, nondimensional density and velocity):
In the above,
is a numerical coefficient which controls the strength of the accretion flow. At its critical value, , is strongest. In the code, is solved for using Eqn. 18 in Bondi's paper.The IC's for this simulation include:
1.291 | |
~1 | |
~1 | |
.14318E+13 | |
25.63 | |
2692.17 |
The case of
flow is an extreme limit for the solution space. This value of has a few interesting features:In other words, when
exactly, we have no accretion flow.Results
case
1.66 | |
.2526 | |
.0128 |
The simulation setup reproduces the correct nondimensional profiles. Here's a comparison of the t=0 nondimensional density and velocity profiles astrobear calculates for the bondi module (left), compared to the Bondi solutions for
(curves II and III for the case of ).The profiles are cut-off within an inner radius of
to avoid extremely high speeds there (am going to get rid of this in the next round of sims). Sampling the mass flux across a spherical shell less than this radius doesn't match up with the theoretical prediction of since the solution is getting stepped on there. Sampling the mass flux across a shell larger than this, however, produces agreement.However, the accretion rate onto the particle does not match the theoretical value. Sampling the mass of the particle over 10 different times shows the accretion rate to be fairly constant at,
(note, the sim was ran for about the freefall time of the average density in the box)
Mesh | ![]() |
Radial velocity | ![]() |
Radial mach | ![]() |
Radial mach | ![]() |
Velocity field | ![]() |
Clipped mass over time (r<1) | ![]() |
Isosurface (r=rsink) | ![]() |
Mass flux (r=rsink) | ![]() |
Library
Attachments (29)
- Bondi_Comparison.png (589.9 KB ) - added by 7 years ago.
- rho_comparison.png (1.4 MB ) - added by 7 years ago.
- vr.png (708.1 KB ) - added by 7 years ago.
- radial_mach.png (1.8 MB ) - added by 7 years ago.
- vec_comparison.png (1.8 MB ) - added by 7 years ago.
- clipped_mass.png (1.1 MB ) - added by 7 years ago.
- mesh_comparison.png (2.7 MB ) - added by 7 years ago.
- massflux.png (687.7 KB ) - added by 7 years ago.
- isosurface.png (1.8 MB ) - added by 7 years ago.
- problem.f90_steadystate (8.6 KB ) - added by 7 years ago.
- physics.data_steadystate (9.8 KB ) - added by 7 years ago.
- problem.data_steadystate (359 bytes ) - added by 7 years ago.
- scales.data_steadystate (619 bytes ) - added by 7 years ago.
- solver.data_steadystate (1.5 KB ) - added by 7 years ago.
- global.data_steadystate (7.9 KB ) - added by 7 years ago.
- Bondi_Comparison_gamma1pt4.png (392.9 KB ) - added by 7 years ago.
- mdot_comp_gamma1pt4.png (1.4 MB ) - added by 7 years ago.
- density_blowup_gamma1pt4.png (1.7 MB ) - added by 7 years ago.
- press_blowout_gam1pt4.png (648.9 KB ) - added by 7 years ago.
- press_spherical_gam1pt4.png (1.1 MB ) - added by 7 years ago.
- plane_comp_gam1pt4.png (1.8 MB ) - added by 7 years ago.
- mdot_sink_gam1pt4.png (828.1 KB ) - added by 7 years ago.
- rho_zoomed_gam1pt4.png (1.1 MB ) - added by 7 years ago.
- press_zoomed_gam1pt4.png (1.1 MB ) - added by 7 years ago.
- rho_lineout.gif (246.7 KB ) - added by 7 years ago.
- press_lineout.gif (252.2 KB ) - added by 7 years ago.
- vrad_lineout.gif (227.1 KB ) - added by 7 years ago.
- press_sonicrad.gif (2.6 MB ) - added by 7 years ago.
- press_sonicrad_zoomout.gif (804.6 KB ) - added by 7 years ago.