[FLASH-USERS] Equilibrium configuration

[Tomasz Plewa]

Jesus -

What you most likely want to resolve is the characteristic pressure
scale height in your problem.

Hope this helps.

Tomek
--
On 3/17/2011 6:20 PM, Jesús Zavala Franco wrote:
> Hi John,
>
> Thank you for your reply, I have tried different configurations and I
> always get the same situation: the gas spreading outwards with
> velocities of ~20 km/s after 300 Myrs of evolution. This happens
> whether I spread the dark matter particles or not. By the way, I tried
> using the point mass potential that is implemented as an option in
> FLASH as you suggested. So I removed the particles completely. I get
> exactly the same situation, so it is not related to the particles.
>
> I'm thinking that the problem is related to what Colin mentioned in
> his answer (check following e-mail)
>
> Cheers,
> Jesus
>
> 2011/3/17 John ZuHone <jzuhone at cfa.harvard.edu
> <mailto:jzuhone at cfa.harvard.edu>>
>
>     Jesus,
>
>     I would actually not expect this setup to work all that well. Most
>     certainly the central cell with the particles and the gas is not
>     going to be in hydrostatic equilibrium. This would be true of the
>     central cell even if you had the dark matter spread throughout,
>     but in that case it would not be much of an issue since what you
>     would get is some minor flattening of the gas density profile near
>     the center.
>
>     But if I read you correctly you have the particles all dropped
>     into this central zone, and the mass of this central zone alone is
>     much larger than the mass of gas in the entire system, which means
>     each of your particles is very massive. What velocities do you
>     have them set to? Even if you set them initially to zero and they
>     are all at the center you're going to get some spurious
>     velocities. Since the particles are so massive the potential is
>     probably changing a lot and this is throwing things out of
>     equilibrium in the center.
>
>     Since the HSE is definitely broken in this cell and probably in a
>     few cells surrounding it, I don't think it's surprising that
>     you're seeing what you are. You are trying to simulate a point
>     mass but severely underresolving it both in terms of spatial and
>     mass resolution. 
>
>     Is there a particular reason you're trying to represent a point
>     mass in this way? There is a point mass gravitational acceleration
>     option in FLASH that would probably be better suited for this
>     purpose. 
>
>     Best,
>
>     John ZuHone
>
>     On Mar 17, 2011, at 12:55 PM, Jesús Zavala Franco wrote:
>
>>     Dear all,
>>
>>     I'm having problems setting up a sphere of gas in hydrostatic
>>     equilibrium under its own gravity + the gravity of a particle
>>     distribution.
>>
>>     In the general case, I would like to have this particle
>>     distribution with the same density profile as the gas
>>     distribution (so I'm aiming at setting up a dark matter halo with
>>     a particle distribution, with gas inside), but to describe the
>>     problem I'm having, I will avoid distributing particles in the
>>     sphere and simply:
>>
>>     1) put 1000 particles in the centre of the sphere
>>     2) put gas distributed spherical around this centre with a radial
>>     density profile (a NFW profile), and pressure given by the
>>     condition of hydrostatic equilibrium:
>>
>>     dP(r)/dr = -(GM(<r)/r^2) * rho_gas(r)
>>
>>     where M(<r) is the total enclosed mass, and rho_gas(r) is the gas
>>     density. M(<r)= M_DM+Mgas(<r), with M_DM the total mass of the
>>     1000 particles, which by the way exceeds the total mass of the
>>     gas by almost an order of magnitude. To solve the equation I
>>     impose a boundary condition outside the sphere setting a pressure
>>     and a density which are reasonable according to the problem and
>>     the density profile I'm putting.
>>
>>     So in short, what I have is a sphere of gas within a
>>     gravitational potential dominated by essentially a point source
>>     in the centre and with a pressure that should give support agains
>>     the gravitational collapse.
>>
>>     I'm using a gird of 8^3 with 4 levels of refinement, an ideal gas
>>     equation of state, a Pfft Multigrid gravity solver, I'm using the
>>     default operator splitting technique to advance the solution.
>>
>>     What I notice is that since the first time step, regardless of my
>>     choice of dtinit, the cells just next to the central cell (the
>>     one containing the 1000 particles), acquire a radial outwards
>>     velocity, whit a size depending of the time step, and that once
>>     the time evolution reaches the typical times of the problem (~100
>>     Myrs), this results in the gas in the inner parts propagating
>>     outwards, reducing the density in the core, after 1Gyr or so,
>>     this propagating gas reaches the boundaries of the sphere. In
>>     other words, the equilibrium set at first is broken.
>>
>>     I have tried using the option ppm_modifystates=.true. since as
>>     described in the user guide:
>>
>>     "The version of PPM in the FLASH code has an option to more
>>     closely couple the hydrodynamic solver
>>     with a gravitational source term. This can noticeably reduce
>>     spurious velocities caused by the operator
>>     splitting of the gravitational acceleration from the hydrodynamics"
>>
>>     I thought this could help, but it didn't. I'm aware that if I
>>     wouldn't put the particles in the centre, this behaviour is just
>>     a resolution problem since the core is not being properly
>>     resolved and the density and enclosed mass is underestimated
>>     there, the pressure is therefore too high (since is initially set
>>     by solving the hydrostatic equilibrium equation with the assumed
>>     analytical profile) and it pushed the gas outwards. However,
>>     since I'm setting a significant gravity source in the center I
>>     wouldn't expect this to be the case. I have tried actually
>>     increasing the mass of the particles by a factor of 10, and not
>>     considering this mass increase in the solution to the pressure
>>     equation, this sets the overall pressure too low and you would
>>     expect a collapse. Even though when at first the velocities of
>>     the contiguous cells to the centre, point inwards, after a while,
>>     they are overwhelmed by an outward flow that develops in the
>>     cells next to these, and to my surprise, the sphere expands as well.
>>
>>     I'm running out of ideas on the initial conditions setup, so I'm
>>     thinking this could either be a resolution issue, or a bad choice
>>     of hydro, gravity solver.
>>
>>     Any hel will be much appreciated. 
>>
>>     Cheers,
>>     Jesus Zavala
>>     Department of Physics and Astronomy
>>     University of Waterloo
>
>
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