Subcritical, subsonic case

General Soln Behavior for this case (different ICs than this run, so just to qualitatively compare):

*Note vr is actually negative for infall

Initial conditions are here: InitialConditions.pdf​

Fixed grid

Fiducial run is at 128³. At this resolution (dx=.03125), the critical radius (rcrit=.0158) is contained within the kernel (r_acc=.125), but below the grid scale (r_min=.027). (Note, r_min is the radial distance between the nearest cell and the sink particle). So, the soln doesn't turn over the way it does in the above plots, at this resolution. Instead, the density and radial velocity are monotonic.

A density comparison of the new algorithm (left) vs. the Krumholz algorithm (right):

Density lineouts comparison-

Mach comparison-

Sink mass vs. time-

However, since the density is going up near the sink particle, implies that the sink isn't accreting 'fast enough'. This is reflected as a decrease in the infall around the sink particle as pressure waves from the increased central density propagate outward:

Testing AMR compatibility

Image comparing 128³ fixed grid (left) vs. 64³ + 1 level (right) 20 frames into simulation (or about 40% the crossing time of a sound wave traveling from the outer fixed boundary to the accretion kernel, i.e. c_s=1 in computatinonal units):

There are only slight differences between the runs (peak density/velocity, e.g.), so this looks pretty good…

Running w/ AMR

To boost runtime speeds, am now switching to testing in AMR…

128 + 1

At 128³ + 1 level, dx_min=0.015625, which means the critical radius (r_crit=.0158) is slightly above the grid scale (r_min=.0135) and contained within the kernel (r_acc=.0625) . (Recall, r_min is the distance of the nearest cell to the sink particle). In the following, can see comparisons to the Krumholz module at the same resolution..

• Note, running the code with the Krumholz algorithm produces 7 frames/minute on 24 cores (Bluehive) compared to the new code, which produces 5 frames/min (both using the optimized version of the code, and identical initial conditions). So the new code is slightly slower…

Density​

Mach​

Radial velocity​

Temperature​

Constants​

Testing 'tweaks'

The following tweaks are modifications to the original algorithm (whose results are given above), in an attempt to improve the internal kernel solution (i.e. maintain the starting upstream steady-state analytic soln to better accuracy) . They are implemented and tested independently of one another…

1) Longer run-time of the 128³+1 sim; does the solution relax to the correct upstream values?

Now running the simulation out to t=0.8 (note, t_{sc}=1 for a sound wave traveling from the fixed outer boundary at r=1 to the accretion kernel).

2) Wider sampling region for calculating shell constants & 3) Larger accretion radius

Density​

Mach​

Vr​

Concerns

-increasing/decreasing Lambda over time?

-mdot onto sink NEQ mass flux into kernel?

-subcycling over kernel before taking hydro step?

-AMR differences in solution?