Re: [FLASH-USERS] 2D multigrid self-gravity in FLASH2.2/2.3

Jason,

In 2D Cartesian coordinates plane-parallel symmetry is assumed, so
the effective Green's function is proportional to ln(r), whereas
what you want is 1/r. For 2D FFT-based Poisson solvers it's pretty
simple to achieve this effect by changing the Green's function, but
the multigrid solver works with the real-space difference equation,
so this route is not available. There has been some work on FFT-
based solvers for FLASH; I'll let others in the know comment.

To do this with the multigrid solver, you would need to run a 3D
simulation with isolated boundaries. This isn't as bad as it sounds:
you can use AMR to refine just the disk plane, so that regions
outside the plane are covered by relatively coarse blocks. You
could try the following parameters, for instance:

Nblockx = 8
Nblocky = 8
Nblockz = 1
lrefine_min = 1
lrefine_max = 6
xmin = 0.
xmax = 6.17E25
ymin = 0.
ymax = 6.17E25
zmin = -3.86E24
zmax = 3.86E24

(This assumes the disk is in the xy plane.) This yields a box that
is (20 kpc)^2 * (2.5 kpc) and has a minimum zone spacing of 9.8 pc
in each direction (effective mesh 2048^2 * 256). Your problem setup
should use a custom version of mark_grid_refinement.F90 to refine
only blocks containing z=0 (as well as the usual 2nd-derivative
criterion). To get higher resolution in x and y without increasing
the number of blocks in z, you would need to increase Nblockx or
Nblocky, or increase nxb or nyb at setup time. Either of these
would increase the size of your base mesh. Increasing lrefine_max
will produce more refinement in z as well, but because of the
refinement pattern that shouldn't be too much of a problem.

Let me know if this solves your problem or if you need more info.

Best,
Paul

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Paul M. Ricker Department of Astronomy
Assistant Professor National Center for Supercomputing Applications
pmricker@uiuc.edu University of Illinois at Urbana-Champaign
http://www.astro.uiuc.edu/~pmricker Urbana IL 61801-3074
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On 30 Jun 2003, Jason Tumlinson wrote:

> Hi,
> I would like to simulate a thin plane of matter (a galactic disk)
> with self-gravity. It seems that no matter what I do in a 2D problem
> the multigrid module returns a gravitational potential that treats
> the problem like a 2d slice of a 3D distribution of matter. For a
> simple test (analogous to dust_coll) the 2d result is exactly the
> analytical solution for a 3D distribution with the same radial
> density dependence.
>
> My questions: Can a true thin plane be treated with the multigrid
> poisson solver? What are the configuration options to do it. If not,
> how can this be done? I am using FLASH2.2, will switching to 2.3 fix
> this problem (I plan to upgrade anyway but wanted to get this worked
> out first).
>
> Thanks,
> Jason
>
>
>
>
Received on Tue Jul 1 11:12:01 2003