update ticket 150

Monopole expansion works in 2.5D

Here is a comparison of phi for the same 2.5D and 3D simulations of a clump at the origin:

The boundary conditions in the 3D case are reflect on the x,y,&z axes, and in the 2.5D are reflect-cylindrical on the r and z axis. For the other box sides, the only possible BC is multipole, which has monopole, dipole, and quadrapole terms possible in 2.5D now (but only monopole in 2D). Both runs use the same solver.

Here is a line out of phi:

You can see they are very close. The spreadsheet curve shows their differences, the highest being inside of the clump, closest near the boundary, and then approaching zero just outside of the clump.

For reference, here is a comparison of the 2D simulation with the 2.5D:

Here, the 2D simulation setup is exactly the same as the 2.5d case, except the boundary condition is plain reflecting, and the solver is structPCG instead of structGMRes (which gave a segfault..). We can see that the 2D self gravity did a worse job of reproducing the full 3D spherical behavior, as expected. Most notably here is the puffier appearance of phi. This is because of the lack of 1/r terms in the stencil in xy space compared to rz space. In rz space, phi is more sharply peaked.

Next steps

This simulation (clump at origin) only produces a monopole term in the multipole expansion, and so we would like to also check the behavior of higher orders terms using different mass distributions.

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