Spherical Mach 10 Wind with AMR
As you can see there are odd features all of the x and y axes of the flow. These features are greatly modifying the flow in an unphysical manner.
Spherical Mach 10 Wind at Zone Center
When that didn't work we tried switching the integrators, the flux upwinding and the slope limiters. None of those appeared to fix the issue. We then moved to a 2-D Cartesian grid to see if the problem was in the source term generator:
Cylindrical Mach 10 Wind on Cartesian Grid
Since the problem still occured we did a carbuncle test by setting up a line wind in cylindrical geometry with a ambient density that contained 1% random flucuations:
Cylindrical Mach 10 Line Wind with 1% fluctuations
Mach 10 Step Jet with a 4 Zone Width
Mach 10 Step Jet with a 7 Zone Width
As you can see the feature, which are the striations at the symmetry axis of the flow after the reverse shock, exists in the 4 zone width jet (which has a 8 zone wide step at the top) but does not in the 7 zone width jet (which has a 14 zone width step at the top).
This is when we decided to try doing non-stepped jets to see if the problem even required steps to exist:
4 Zone Wide Mach 10 Jet Launched from Boundary
6 Zone Wide Mach 10 Jet Launched from Boundary
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep
6 Zone Wide Mach 10 Jet Launched from 1 Zone Deep
8 Zone Wind Mach 10 Jet Launched from 1 Zone Deep
We found that for jets larger than 4 zones launched from the boundary and jets larger than 6 zones launched from 1 zone deep the jets were fine (the feature may still be there in the 6 zone wide jet launched from the boundary and the 8 zone wide jet launched 1 zone deep but I can't really tell).
We noticed that the double horned structure (bunny ears) seen in the 4 zone jets was present after a few time steps (see the line cut below) and that it got amplified as the jet accelerated. We also noticed that the modification appeared to be occurring in the density as well. In fact the modification of the density was the largest contributor as to why the structure exists as it does. Below are images of the density and the density times the magnitude of the velocity (the momentum density) for the 4 zone wide jet launched from 1 zone deep. Also included is a line cut from the 10th time step across the zones which are directly in front of the jet enforced region (i.e. 2nd zone in). The line cut is included to show what the profile of the flow looks like at early time. Especially its included to show that the velocity has the double horned feature seen later in the flow and that the momentum density is flat and therefore the modification must be occuring to the density, at least initially:
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, Line Cut at 10th timestep
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, Density
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, Momentum Density
We did analogous runs in the MHD-TVD code which are below and had a feeling that it might be that some detail of dimensional splitting was left out of AstroBEAR namely:
1. Enforcing Boundaries and User Defined Enforced Regions after every directional pass.
2. Enforcing the same time step for each permutation of the directional passes.
4 Zone Wide Mach 10 Jet Launched from Boundary, TVD
6 Zone Wide Mach 10 Jet Launched from Boundary, TVD
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, TVD
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, Line Cut at 2nd timestep, TVD
However after implementing these fixes the problem still occured. Tom had been launching his jets impulsively into the medium when he was doing his TVD runs so I decided to match that with AstroBEAR and found that an impulsively launched jet, as opposed to one with a ramp, fixed the problem:
4 Zone Wide Mach 10 Jet Launched Impulsively from 1 Zone Deep
I will now redirect your attention to the 2 below images of the 4 zone wide 1 zone deep TVD run:
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, TVD
4 Zone Wide Mach 10 Jet Launched from 1 Zone Deep, Line Cut at 2nd timestep, TVD
Originally when we looked at this simulation we only looked at the initial evolution which looks rather similar to the AstroBEAR evolution as demonstrated in the line cut at early time. However, at late time the double horned feature disappears and the jet changes into a reasonable flow. This may hold the key as to what is truly going on.
Spherical Mach 10 Wind Launched Impulsively
Spherical Mach 10 Wind Launched Impulsively Zoomed in at 90 degrees
Spherical Mach 10 Wind Launched Impulsively Zoomed in at 0 degrees
Spherical Mach 10 Wind Launched Impulsively at Timestep 505
You will notice that the features are still there (Note: The first 3 images are at an earlier time so the features have not fully grown). For comparision we put together a wind in the MHD-TVD code (Note: This wind is on a Cartesian Grid):
Cylindrical Mach 10 Wind Launched Impulsively using TVD
Cylindrical Mach 10 Wind Launched Impulsively using TVD Zoomed in at 90 degrees
Cylindrical Mach 10 Wind Launched Impulsively using TVD Zoomed in at 0 degrees
Since no problems occured we decided to do a wind with the TVD code that had an exponential ramp as before:
Cylindrical Mach 10 Wind with Exponential Ramp using TVD
It seems that MHD-TVD does not show the same issues as AstroBEAR for this problem which leads us to believe that it is a difference between AstroBEAR and MHD-TVD the make the problem disappear. As it stands we have no idea as to what that could be.
We decided to do an exponential ramp run with AstroBEAR as well for comparision to the previous run with out the corrections made to the direction split method. Below are two images the first without the corrections, the second is with the corrections:
Spherical Mach 10 Wind Without Corrections
Spherical Mach 10 Wind With Corrections
As you can see there really isn't much difference between to two. Still we feel that the corrections should be implemented just in case any future problems arise.
Earlier we mentioned that it appears to be the density that is seeding the problem. I decided to go and see if I couldn't find the very first step where the problem started occuring for the corrected exponential ramp wind. Below are a series of images taken at both 90 and 0 degrees for density, speed and momentum density:
Spherical Mach 10 Wind at Timestep 150 at 90 Degrees, Density
Spherical Mach 10 Wind at Timestep 150 at 90 Degrees, Speed
Spherical Mach 10 Wind at Timestep 150 at 90 Degrees, Momentum Density
Spherical Mach 10 Wind at Timestep 150 at 0 Degrees, Density
Spherical Mach 10 Wind at Timestep 150 at 0 Degrees, Speed
Spherical Mach 10 Wind at Timestep 150 at 0 Degrees, Momentum Density
It appears now that the density shows no sign of the problem but the momentum density does, the features in this case are decrements in the velocity which are either along the axis in the case of 0 degrees or bracketing the axis like the bunny ears earlier for 90 degrees. I'm not quite sure what to make of this as I am sure that when we started to look into this problem we found that the density was the first thing to go bad and not the momentum density.
4 Zone Wide Mach 10 Jet Lauched 1 Zone Deep with ViscCD at 1
As you can see the problem is gone from this run. I then did a spherical wind test with ViscCD equal to 1 and then 2:
Spherical Mach 10 Wind at Timestep 553 with ViscCD at 1
Spherical Mach 10 Wind at Timestep 553 with ViscCD at 2
In the first image the problem is different from before but still there. However in the second image with ViscCD set to 2 the problem disappears. It seems that Andy was right and the problem was just a carbuncle. I would suggest the all future runs use ViscCD equal to 2 to suppress this issue. Thanks for all your help.
