Origin of Rapid Acceleration Between Timesteps

[hwhitehead]

This problem is potentially related/is a continuation of issues introduced in post.

Specifically, my simulation experiences an error where a small amount of gas is rapidly accelerated. This acceleration does not appear to be a direct effect of the custom sourcing terms (frame forces and the softened gravitaitonal potential of a massive object).

Analysis of the maximal velocity in the simulation before and after the source terms are applied (by comparing CONS before user source terms to CONS after), shows that the source terms do not directly lead to this rapid acceleration. However, when observing the CONS velocity at the start of the next source application (one timestep later), the maximum velocity is massively increased.

To demonstate, I attach two output logs. The first shows a 'normal' period of evolution:

the velocity changes between timesteps are moderate. v_max barely changes during sourcing as the acceleration is acting on gas in circular orbits about the gravitating bodies.

The second panel shows the error developing:

The velocity changes due to the sourcing is still moderate, but now the velocity changes between timesteps is massive. The timesteps themselves are also reducing in accordance with the CFL constraint. We don't see any massive drops in density however.

What could explain such a massive increase in velocity within a small timestep? The maximum acceleration that can be applied by the gravitational source term is ~1e3. The observed acceleration is of order 1e8 for comparison.

My current guesses:

1. an extreme density contrast: as I am using an isothermal EOS, if there arises a strong density contrast, there should be a very high pressure gradient. Such a gradient should not arise naturally, but may be evidence for a different numerical issue
2. viscosity: I am using a viscous prescription. Is it possible for very large acceleration to be exterted if there is an extreme velocity gradient in the simulation? I would not have thought this to be possible on such short timescales however. If the flow is very chaotic and there are fast moving flows coming into contact, this might be possible.

If anyone has experienced an issue similar to this before, please let me know. I can provide more data/routine specifics if needed.

Some details on the error: the error arrives when the flow near the gravitating source is very chaotic, suggesting a possible connection to strong gradients. It is hard to predict when/if such an error will occur: some potential 'fixes' to the system just create an alternative flow that avoids the error and do not guaruntee that the issue will be fixed generally (which I require). I am using the rk2 solver with xorder = 2.

[hwhitehead]

Closer inspection of the system points to a correlation with strong density gradients, though it is currently unclear to whether this is the cause, or result of the rapid acceleration.