[FLASH-USERS] Biermann Battery in 2D and 3D geometry

[Benjamin Spiers]

Dear FLASH users, developers,

The issue Xavier reports resembles one I’ve noticed recently, and have been trying to track down. It seems to be caused by the fact that the Biermann source term implementation updates the cell-centred magx/y/z variables but not the face-centred magnetic fields. Assuming I’m understanding how the code treats MHD correctly, the main loop of the simulation does something which approximates


  1.  Solve MHD equations (updates face-centred B fields in divergence-free way)
  2.  Set cell-centred mag variables by averaging face-centred quantities to cell centres
  3.  Update mag variables using Biermann source
  4.  Output plot files etc.

I think what happens is that step 2. overrides the effect of step 3 on the previous loop iteration (which doesn’t happen in 2D because step 2 doesn’t touch magz in two dimensions, presumably because there aren’t really meaningful z-‘faces’ in x-y geometry). I guess the fix is to update the face vars in the 3D source term implementation, but that would presumably need some caution to make sure the divergence-free constraint is still obeyed.

The upshot of all this is that the magnetic field values seen in the plot files are presumably just dB/dt multiplied by a single time-step rather than the actual B values generated over multiple time steps.

Best wishes, and I hope this helps to fix the issue,

Ben

From: flash-users-bounces at flash.uchicago.edu <flash-users-bounces at flash.uchicago.edu> On Behalf Of Xavier Ribeyre
Sent: 14 January 2021 09:33
To: flash-users <flash-users at flash.uchicago.edu>
Subject: [FLASH-USERS] Biermann Battery in 2D and 3D geometry

Dear FLASH Code users,

In the FLASH version 4.6.2 there is two Biermann battery test cases.
One in 2D cartesian geometry and one in 2D axis-symmetric (cylindrical) geometry.

1- Whatever in 2D Cartesian or 2D axis-symmetric cases: the magnetic z component is the same.
And there is no magnetic field variation whatever I activated the
"source BB terms" or the "3T BB term": i.e in flash.par:
(use_Biermann3T = .false. hy_biermannSource = .true.
or use_Biermann3T = .true.  hy_biermannSource = .false.)
The z component values of the magnetic field magz are the same. This behavior is correct.

-However it seems that the SIGN of the magz component is not correct in 2D axis-symmetric case (it is the opposite).
Are you agree with that?

2- I did the same test case in 3D geometry with the the same temperature and density profile.

When I deactivated the source term
i.e. use_Biermann3T = .true. hy_biermannSource = .false. in the flash.par
The values of magz seems correct (if we compare with the 2D previous cases)
BUT
When Biermann source term is activated:
i.e. use_Biermann3T = .false. hy_biermannSource = .true. in flash.par
then now the magz values are very different and very low (20 times lower).

-I don't know why there is a discrepancy between these two 3D simulations

I hope you can help to understand what happens.

Best regards,

Xavier Ribeyre



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