# [FLASH-USERS] Interpreting pressure behavior in the SinkRotatingCloudCore test problem

Sasha Tchekhovskoy atchekho at northwestern.edu
Mon May 27 23:58:26 CDT 2019

```Hi Sarah,

My experience with negative pressures mostly comes from trial and error
approach. Here is an example of how negative pressures can emerge in
supersonic flows even without any discontinuities:
http://adsabs.harvard.edu/abs/2007MNRAS.379..469T . For instance, Sec. 5.1
and Fig. 3 illustrate what happens to a simple 1D Hubble-like expanding
flow: density, pressure, and internal energy are uniform, and velocity is
linear in x. The correct solution is for density and internal energy to
smoothly decrease in time. However, the truncation error of the numerical
scheme tends to always has the same (negative) sign. This causes the
internal energy and pressure to decrease much more than they should,
essentially without bound.

The negative pressures themselves do not typically cause problems: if there
is a cell with a negative pressure, it could be fixed by resetting its
pressure (and, correspondingly, internal energy) to a small positive value.
Since the pressure in the "fixed" cell is smaller than in the surrounding
cells, its value does not really matter. However, herein lies a potential
problem: this approach injects energy into the simulation, i.e., the total
energy is no longer conserved. In some cases, this might lead to a runaway
instability that eventually causes the simulation to crash.

How can the instability happen? Oftentimes, it is the same cell that keeps
developing a negative pressure. The pressure keeps getting negative because
the truncation error leads to energy fluxes out of the cell taking more
energy to neighboring cell(s) than they should. Thus, the energy that we
add to the problematic, negative-pressure cell gets "vacuumed out" into the
adjacent cells. These adjacent cells can get hotter in a runaway fashion;
in fact, they can become unphysically hot and destroy the entire solution.

We experienced such instabilities in simulations that were part of this
work: http://adsabs.harvard.edu/abs/2014MNRAS.445.3919K . If I remember
correctly, smoothing the initial jump in density (so it is well-resolved on
the grid), using an unsplit integrator, increasing resolution, and
decreasing the time step in Athena helped us to alleviate this problem. In
my experience, such problems tend to appear at high Mach numbers and/or in
the presence of large density and/or pressure contrasts.

Best,
Sasha

On Mon, May 27, 2019 at 9:17 PM Sarah T. Stewart <sts at ucdavis.edu> wrote:

> Hi Sasha, & co.
>
> I am also observing a strange phenomenon with energy transport in a
> rotating, self-gravitating system with strong shear in the velocity field
> in a finite volume code.
>
> Can you point me to any papers that discuss errors/problem/issues with
> studying shearing rotating systems in finite volume codes?
> Thanks,
> Sarah
>
> On Mon, May 27, 2019 at 7:08 PM Sasha Tchekhovskoy <
> atchekho at northwestern.edu> wrote:
>
>> I do not have much experience with FLASH specifically, but with other
>> finite volume methods such as Athena or HARM, one can get very low or
>> negative pressure regions along discontinuities (e.g., shear
>> discontinuities or shocks), especially if the density contrast at the
>> discontinuity is substantial and/or if supersonic flows are involved. One
>> way to look at this is near the discontinuity the scheme reduces to low
>> (first) order, and the increased numerical truncation error ends up
>> contaminating the smallest quantity, which is typically the thermal
>> pressure.
>>
>> I agree that seeing maps of density and velocity could be helpful to get
>> a sense of the expected force balance at the discontinuity. Maybe even 1D
>> slices in addition to 2D maps.
>>
>> Best,
>> Sasha
>>
>>
>> On Mon, May 27, 2019, 19:42 Ryan Farber <rjfarber at umich.edu> wrote:
>>
>>> Hi Sean,
>>>
>>> I'm not familiar with that problem so you'll hopefully get a more useful
>>> answer from someone else. But until then, I have some thoughts below which
>>> I hope might help.
>>>
>>> First, this made me think of Jaehan Bae's work regarding the spiral
>>> density wave instability. However, I believe that only happens when there's
>>> a planet/object orbiting the (proto)star (what happens is that multiple
>>> gaps in the disk appear despite there being only one object, implying that
>>> HLL Tau's many gaps don't necessarily mean it has that many planets). I
>>> only remember seeing movies of density but I would think the low density
>>> region would also be low pressure).
>>>
>>> Speaking of which, it might be useful to see density and temperature
>>> plots as well to understand in which (or both) variable causes the low
>>> pressure you're seeing.
>>>
>>> Other thoughts:
>>> Is there an analytic solution to your problem (or a simplified version
>>> of it) to compare to? Absent that, you could try a different EOS solver.
>>> You could also experiment with the hydro solver (if you're doing hydro,
>>> trying the (un)split solver; different Riemann solver).
>>>
>>> If all those look the same then I would think it's something physical.
>>> If you have checkpoint files at 34,50 kyr then you can look at ACCX, ACCY,
>>> ACCZ (check Flash.h if I spelled them right; I'm traveling currently) to
>>> see if your low pressure region is in force balance, explaining it's
>>> persistence. It may also help to consider the centrifugal, gravitational,
>>> and pressure gradient forces individually.
>>>
>>> I'm assuming SinkRotatingCloudCore uses self-gravity; is that in fact
>>> the case? Does it use radiative cooling? If so, you might want to also try
>>> turning cooling off to simplify things a bit.
>>>
>>> Best,
>>> Ryan
>>>
>>>
>>>
>>> Sent from my iPhone
>>> On May 25, 2019, at 11:59 AM, Lewis,Sean <scl63 at drexel.edu> wrote:
>>>
>>> Hello all,
>>>
>>>
>>>
>>> In my work towards modeling a protoplanetary disk, I have consistently
>>> encountered an interesting behavior in gas pressure. Specifically, a region
>>> of low pressure around the collapsed cold gas cloud that is generally about
>>> 10x lower than the pressure of the outer regions of the cloud as well as
>>> the surrounding less-dense gas. I have attached a few .png files from the
>>> out-of-the-box SinkRotatingCloudCore test problem to illustrate what I
>>> mean. The images are taken at 34kyr and 50kyr taken looking down the
>>> z-axis, and another 50kyr snapshot looking down the x-axis to see the
>>> side-view of the forming disk.
>>>
>>>
>>>
>>> How can this effect be interpreted? Something physical that’s expected?
>>> Something numerical that is (un)expected? Initially, I thought that the
>>> dense gas cloud was contracting towards its center of mass faster than the
>>> surrounding halo gas, creating a vacuum of sorts. However, I have seen the
>>> same effect in other simulations of mine where the dense gas is nearly
>>> relaxed into a disk though to a lesser degree and the same effect is not
>>> seen in plots of the gas density. This makes me think this could be an
>>> artifact of the equation of state solver in some way.
>>>
>>>
>>>
>>> With appreciation,
>>>
>>>
>>>
>>> Sean Lewis
>>>
>>> Drexel University
>>>
>>>
>>>
>>>
>>>
>>> <pres34k.png>
>>>
>>> <pres50k.png>
>>>
>>> <pres50k_x.png>
>>>
>>> --
> Sarah T. Stewart
> Professor, Dept. Earth and Planetary Sciences, UC Davis
> 530.794.8689  sts at ucdavis.edu  @SarahTStewart
> sarahtstewart.net
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