[FLASH-USERS] Checkboard of Magnetic Monopoles

Tue Apr 17 23:40:02 EDT 2012

Aaron,

> Update:
>
> The monopole checkerboard is only present when using the USM solver, the
> 8wave solver is unaffected.

This is very true because the USM solver is very sensitive to divB
initialization and is a very different scheme than the 8wave solver. In
general, the monopole issue you're seeing is mostly caused by the wrong
initial condition or the boundary conditions of the cell
interface-centered magnetic fields (facevars in the code).

The USM solver treats divB using the so-called constrained transport
method which makes sure that divB~10^(-12) or lower providing machine
accuracy in handling the divB constraint on a staggered grid. It will
remain to be such a small magnitude ONLY IF the initial divB is ~
10^(-12); otherwise it will grow.

The 8wave solver doesn't need such careful divB initializations nor
preserve divB. The scheme just advects the monopole effects out of the
domain without accumulating them. And divB ~ 10^(-1) or so.

> None of the following numerical parameters
> have any affect on the structure of the checkboard: number of guard cells,
> solver order, E_modification, energyFix, prologation method, Riemann
> solver, nblockx, boundary conditions, computational volume, and cooling
> rate.

Can you please check if your initial divB is small too? Do you have any
special boundary conditions? In general, if you can tell me more about
your simulation along with your log file and flash.par, it will be helpful
to understand the issue better.

> The monopoles typically appear in the top right quarter of each
> CPU's domain, but can vary slightly (see pictures).

Best,
Dongwook

> ________________________________________
> From: Nathan Goldbaum [goldbaum at ucolick.org]
> Sent: Tuesday, April 17, 2012 2:29 PM
> To: Aaron Froese
> Subject: Re: [FLASH-USERS] Checkboard of Magnetic Monopoles
>
> Hi Aaron,
>
> This is a wild guess, but I think the error you're seeing is because
> you're not including the magnetic energy when you update the solnData
> vector.
>
> Instead of
>
> solnData(ENER_VAR,i,j,k) = ei + ek
>
> You should have
>
> solnData(ENER_VAR,i,j,k) = ei + ek + emag
>
> where
>
> emag =
> .5*dot_product(solnData(MAGX_VAR:MAGZ_VAR,i,j,k),solnData(MAGX_VAR:MAGZ_VAR,i,j,k))
>
> I suggest you look closely at hy_uhd_energyFix.F90 (located in
> source/physics/Hydro/HydroMain/unsplit/MHD_StaggeredMesh/) before you make
> further modifications.
>
> Hope that helps!  If any other users of the unsplit solver have a more
> solid understanding of what's happening in Aaron's simulation, please
> chime in.
>
> Cheers,
>
> Nathan Goldbaum
> Graduate Student
> Astronomy & Astrophysics, UCSC
> goldbaum at ucolick.org
> http://www.ucolick.org/~goldbaum
>
> On Apr 17, 2012, at 2:20 PM, Aaron Froese wrote:
>
>> Hi Mark,
>>
>> I have been able to recreate the checkboarding problem on the OrszagTang
>> example using the USM solver.  I have included the necessary changes,
>> which just involve including a modified cooling module to reduce the
>> local internal energy by a small factor each time step.  I have included
>> plots of divB at the first checkpoint for two cases: one with a static
>> AMR and the internal energy dropping by a factor of 1e-6 each time step,
>> the other with a dynamic AMR and the internal energy dropping by a
>> factor of 1e-3 each time step.  The monopoles always appear on the
>> borders of 8x8 squares.
>>
>> Thanks,
>> Aaron
>> ________________________________________
>> From: Mark L Richardson [Mark.L.Richardson at asu.edu]
>> Sent: Thursday, April 12, 2012 4:20 PM
>> To: Aaron Froese
>> Cc: flash-users at flash.uchicago.edu
>> Subject: Re: [FLASH-USERS] Checkboard of Magnetic Monopoles
>>
>> Hi Aaron,
>>  Are you able to overlay the grid so we can see how these features
>> relate to the blocksize?
>>
>> Cheers,
>>  -Mark
>>
>> On Thu, Apr 12, 2012 at 3:54 PM, Aaron Froese
>> <aaron.froese at generalfusion.com<mailto:aaron.froese at generalfusion.com>>
>> wrote:
>> I am using the USM MHD solver with flash3 and I noticed that I am
>> getting very large magnetic monopoles appearing in my solution, of the
>> same order as the magnetic fields.  The monopoles appear in a somewhat
>> random checkboard-like pattern, which I believe has something to do with
>> the block-structure of the mesh.  I have attached two plots which show
>> the magnitude of divb and posted copies online in case the mailing list
>> does not allow file attachments.
>>
>> Cylindrical Shell Compression 2D - abs(divb)
>> http://oi40.tinypic.com/1zeihbp.jpg
>>
>> Spherical Shell Compression 3D - abs(divb)
>> http://oi39.tinypic.com/34grldv.jpg
>>
>> The central circle where the checkboard pattern appears is the only
>> volume that is magnetized.  I am using a static AMR mesh with a uniform
>> resolution across the magnetized volume, and less refinement in the
>> surrounding non-magnetized fluid.  Has anyone observed similar
>> behaviour?  It is definitely numerical in nature, but I do not know what
>> part of the code is responsible..
>>
>> Thanks,
>> Aaron
>>
>>
>>
>> --
>> Mark Richardson,
>> Mark.L.Richardson at asu.edu<mailto:Mark.L.Richardson at asu.edu>
>> Ph.D. Candidate: Astrophysics
>> PSF 271
>> School of Earth and Space Exploration
>> Arizona State University
>> 480 318-4449
>> www.public.asu.edu/~mlricha4<http://www.public.asu.edu/~mlricha4>
>>
>>
>>
>> !DSPAM:10175,4f8ddebf128361398417114!
>> <OrszagTang-Cool-AMR_abs-divb.png><OrszagTang-Cool-uniform_abs-divb.png><Cool.F90><Config>
>
>