wiki:u/erica/AccretionModelingBlog

Version 16 (modified by Erica Kaminski, 7 years ago) ( diff )

Bondi Accretion

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 following are the fiducial IC's used in the simulations (in computational units), unless otherwise noted:

Lx=Ly=Lz 20
Mx=My=Mz 64
MaxLevel (AMR) 2
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.

Additionally, the following sims use (unless otherwise noted):

1.291
~1
~1
.14318E+13
25.63
2692.17

Research Log:

3/18/18, , dynamical cases

Resolving sonic point

Not-resolving sonic point

3/18/18, , steady-state case

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.

In addition to the Bondi/flow params cited in the top section of this page, the sim was setup using the following (in CU):

1.66
.2526
.0128

Note, the sonic radius is not resolved by about a factor of 20 in this simulation, as seen when checking dx quoted above.

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 (2689 compared to 2692).

Since the solution is getting stepped on within some small inner radius, can't meaningfully check the behavior of the accretion algorithm and any spurious waves it might be generating there. Instead, will be removing this inner boundary in the next run. Would like to test the effect of the sonic radius being outside of the accretion radius as opposed to within. To test this will do a resolution study on flow, where the sonic point is .

As the following images show, this set of conditions produces a steady state solution… Both the sonic point is not-resolved, as well as the solution is being stepped on where non-steady effects could happen due to effects of the accretion algorithm. The attached module files that produce these files are thus called "*_steadystate*"

Mesh
Radial velocity
Radial mach
Velocity field
Isosurface (r=rsink)
Mass flux (r=rsink)

Library

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