ALJ 2D energy conservation test

[joaander]

Description

Add long running NVE simulations for ALJ particles in 2D (hexagons).

Motivation and context

Replace the shorter version of this test previously housed in HOOMD-blue: glotzerlab/hoomd-blue#1428

How has this been tested?

Output:

Data is available to Glotzer group members in /nfs/turbo/glotzer/hoomd-validation/alj-2d/2022-11-18.

Checklist:

• I have reviewed the Contributor Guidelines.
• I agree with the terms of the HOOMD-blue Contributor Agreement.
• My name is on the list of contributors (CONTRIBUTORS.md) in the pull request source branch.

[joaander]

Energy conservation is good, momentum conservation could be better. However, this is in line with the results we got when writing the ALJ paper. There are inherent small discontinuities that cannot be avoided.

[tommy-waltmann]

I have one comment that could make the code a bit cleaner. Also, why are the changes in linear momentum so discrete compared to the changes in energy?

[joaander]

I have one comment that could make the code a bit cleaner. Also, why are the changes in linear momentum so discrete compared to the changes in energy?

While the energy as a function of the relative positions and orientations of the particles is continuous, the torque and direction of the force are not. Discontinuities in the force violate the assumptions of the numerical integration method which leads to problems like this. From the jumps in the momentum, it seems that there are certain types of collisions that lead to large errors but the vast majority of particle collisions are fine. @vyasr and I worked a lot on this in the implementation and this is the best we could do.