Tracking the mass that falls onto the BE sphere

I would like to calculate the mass that falls onto a shell of dr=0.1RBe at r=Rbe from the ambient over the course of a simulation. There may be a few ways to do this, but easiest may be what came to mind today: find M(t) of the sphere with r=1.1Rbe, using Visit's query option for total mass in box.

The method

First, I had to determine the right sum to use in Visit. I see that the 'query' option had 2 sums: weighted and not. Additionally, I found that the sum query is for the current plot. If that plot is a slice of the full simulation, the query will return only a sum of variables from that slice's mesh. Using my knowledge of the BE sphere's total mass from my simulation output —- that is, 151 solar mass, I calculated the mass of the ambient quite easily, given the ambient is of uniform density:

amb = (L^3 - {4\over3} * r^3 * \pi) \rho

Putting this into computational units, I discovered that weighted variable sum was the correct query to get the total rho/cell (and hence mass) in the grid.

The plan was to calculate M(t, 1.1Rbe) using the following formula:

(t, 1.1Rbe) = Mtotal(t)-Mambient(t)

I knew I could query-over-time the Mtotal and perhaps make a clip of the box that would isolate only the ambient, and then query-over-time the Mambient. However, I checked first whether I could just treat Mambient as constant. A movie showing rho(t) of just the ambient indicated I could:

Considering the Mtot=Mtot(t) as given by Visit's query:

I was curious where the change in mass was occurring. Since the density of the ambient, and its volume is staying constant, must be inside of the sphere… Here are some plots of the density inside of the sphere at different times:

So, the density is changing, but is the total mass? Visit can integrate these curves, and indeed the area under the curves were different, indicating a change in the total mass of the sphere.

Thus, it seemed justifiable to make the assumption: 1) mass of ambient stays constant, 2) calculate M(t) of the sphere with r=1.1Rbe using the Mtot query of visit.

Using this data, I found the following curve for M(t) of this sphere:

I see that Mbe crit is below the minima of M(t). This is no doubt due to some SMALL round-off error somewhere in computing the total masses in the grid. If for instance, I use simply the formula above to find the mass of the BE sphere, it does not give me exactly what my code gives. The Visit calculation gives me ~0.78 whereas my code says it is ~0.72 — in line with the Crit Mbe as expected.

Now, it should also, be noted that the crit Mbe is computed by the formula:

(t, 1.1Rbe) = Mtotal(t)-Mambient(t) }}}. This describes __ blah blah, whereas my sphere is _blah Blah. I guess what can be taken home safely from this curve is that M(t) does not fluctuate wildly, and never goes more than 10% over the crit Mbe.