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<div><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Hello Hayley,</span></div>
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Thanks for letting us know about this issue. Since this was not a problem in earlier versions of the Einstein Toolkit, could you check out older ET versions and find when this change appears? It would be helpful if we knew that this was introduced in the
changes from ET_2020_05 to RT_2020_11, for example. Then, we can focus on how the thorns changed between those two releases.</div>
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Also, are you using the FRLWSolver<span style="color: rgb(0, 0, 0);"> in the Toolkit, or a newer in-house version?</span></div>
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<span style="font-family: Calibri, Helvetica, sans-serif, serif, EmojiFont; font-size: 16px;"> Samuel Cupp
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<span style="font-family: Calibri, Helvetica, sans-serif, serif, EmojiFont;"> Postdoctoral Researcher<br>
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<span style="font-family: Calibri, Helvetica, sans-serif, serif, EmojiFont;"> Department of Physics</span></div>
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<span style="font-family: Calibri, Helvetica, sans-serif, serif, EmojiFont; color: rgb(0, 0, 0);"> University of Idaho</span></div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Users <users-bounces@einsteintoolkit.org> on behalf of Hayley Macpherson <hayleyjmacpherson@gmail.com><br>
<b>Sent:</b> Thursday, November 9, 2023 3:28 PM<br>
<b>To:</b> users@einsteintoolkit.org <users@einsteintoolkit.org><br>
<b>Subject:</b> [Users] "Spikes" in density for FLRWSolver single-mode simulation</font>
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<div class="" style="word-wrap:break-word; line-break:after-white-space">Hi all,
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<div class="">I’ve noticed an issue with the single-mode setting of FLRWSolver (cosmological initial data thorn) when evolving with GRHydro. </div>
<div class="">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). </div>
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<div class="">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. </div>
<div class="">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. </div>
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<div class="">I’ve attached a parameter file which will reproduce the problem I’m seeing (which initialises the figure shown below). </div>
<div class="">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. </div>
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<div class="">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. </div>
<div class="">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. </div>
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<div class="">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. </div>
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<div class="">If anyone is able to help me I would very much appreciate it!</div>
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<div class="">Best wishes,</div>
<div class="">Hayley</div>
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<div>Hayley Macpherson | NASA Einstein Fellow</div>
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<a href="mailto:hjmacpherson@uchicago.edu" class="">Email: hjmacpherson@uchicago.edu</a></div>
<div>Pronouns: she/her/hers<br class="">
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Office: ERC 479<br class="">
Kavli Institute for Cosmological Physics<br class="">
Eckhardt Research Center<br class="">
5640 South Ellis Avenue<br class="">
Chicago, IL, 60637</div>
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