[Users] "Spikes" in density for FLRWSolver single-mode simulation

[Hayley Macpherson]

Hi all,

I’ve noticed an issue with the single-mode setting of FLRWSolver (cosmological initial data thorn) when evolving with GRHydro. 
This set up is three intersecting sine-waves in 3D, see the attached 1D slice for the relative density perturbation (delta = rho / rho.mean - 1) on the initial slice (first plot attached). 

To do cosmological simulations which are dark-matter dominated we want something as close to P=0 as possible. GRHydro does not allow this so instead we choose a pressure such that P<<rho. Specifically, we choose a Polytropic EOS with poly_gamma=2 and set poly_k to be very small to achieve this. This has worked in the past, but recently I’ve noticed something strange in the perturbations themselves. I have previously used this setup back in 2017 and didn’t notice this issue, so I’m unsure if it’s something in a recent version of the ET or something different in the parameter file I’m setting. 
Also just to note - I am aware that Eloisa’s code allows for P=0, however, having a small amount of pressure in the simulations is actually beneficial at late times when the structures are nonlinear (it stops the code from crashing too early and allows us to get further into the nonlinear regime). So for this reason I prefer to continue using GRHydro for now. 

I’ve attached a parameter file which will reproduce the problem I’m seeing (which initialises the figure shown below). 
The second plot I’ve attached shows the same simulation 5 iterations later (the 1D slice is 1/4 of the way through the domain, at index 8 in this example), where at the base of the sine wave you can see the “spike” starting to grow. This continues to grow throughout the simulation to be very large (the last plot is the same simulation after 400 iterations, for example). Also to note, this perturbation is small enough such that for the entire simulation it *should* remain very closely approximated by a sine wave. 

I’ve pinpointed this issue to be sensitive to the value of poly_k that I choose for the simulations. Changing the value of poly_k changes the time in the simulation at which this occurs (it happens later on for larger values of poly_k), but then we reach a point at which the P<<rho condition we require is not satisfied anymore for large values of poly_k. I’ve chosen an extreme value of poly_k in the attached parameter file so that the problem happens early on and it might be easier to diagnose. 
It seems like this is occurring at the minima and maxima of the sine wave, so I thought it might be something related to the fact the derivatives are very small at these points with a small poly_k such as we’re choosing. 

I thought that instead of trying to find the “sweet spot” where that these spikes don’t occur *and* we can satisfy P<<rho, there might actually be a fix from someone who knows GRHydro much better than I do. 

If anyone is able to help me I would very much appreciate it!

Best wishes,
Hayley










----

Hayley Macpherson | NASA Einstein Fellow

Email: hjmacpherson at uchicago.edu
Pronouns: she/her/hers

Office: ERC 479
Kavli Institute for Cosmological Physics
Eckhardt Research Center
5640 South Ellis Avenue
Chicago, IL, 60637

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