Wind Disk Interacion

Conservation of Angular Momentum

2D Results

While the code conserves momentum, it does not explicitly conserve angular momentum. To test this we setup a 2D disk around a point gravity source with a density contrast of 100. Pictured below is the angular momentum. The left panel has a truncated color scale to show the effects of periodic boundaries as well as the transport of angular momentum from the disk into the ambient. Also shown are contours of angular velocity corresponding to .5, 1, and 2 rotations over the course of the simulation. The right panel is a zoom of the disk itself without a truncated color scale. Here is the movie​

We also did an explicit query of the total angular momentum as a function of time. Over the course of the simulation the total fractional change in angular momentum is only .00081 or less then .1% It is likely that the loss of angular momentum is due to numerical dissipation at the center of the disk, although with levels so small it is difficult to rule out boundary effects. Although the symmetry of the problem should keep the net angmom transport from the boundaries to zero.

3D Results

We then extended the simple disk into 3D neglecting pressure support in the z direction. First we used no gravitational softening. The large diffusion of angular momentum at the origin produces heat that leads to jets.

movie​	movie​

Next we used gravitational softening at a radius of 20 computational units or 8 cells. This suppressed any jet

movie​	movie​

We then increased the resolution by 2 and decreased the softening radius to 5 computational units or 4 cells. No jet forms although there is a hot halo.

movie​	movie​

We then compared the 3D results to a 2.5D run with the same setup.

movie​ (left panel is 3D, right panel is 2.5D)	movie​ Red is density and blue is Angular Momentum. Solid is 2.5D and dashed is 3D

And finally compared the total z component of the angular momentum of the 2.5D run (red) with the 3D runs with no gravitational softening (blue) and with 4 cells of gravitational softening (green). They are all within a few percent and the boundaries may be playing a small role as angular momentum can be lost/gained from the reflecting boundaries. However the increased loss of angular momentum for the 3D run with no softening (blue) is consistent with the presence of a jet and the diffusion of angular momentum at the origin.