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<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Dear FLASH users, developers,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">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<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<ol style="margin-top:0cm" start="1" type="1">
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span style="mso-fareast-language:EN-US">Solve MHD equations (updates face-centred B fields in divergence-free way)<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span style="mso-fareast-language:EN-US">Set cell-centred mag variables by averaging face-centred quantities to cell centres<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span style="mso-fareast-language:EN-US">Update mag variables using Biermann source<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span style="mso-fareast-language:EN-US">Output plot files etc.<o:p></o:p></span></li></ol>
<p class="MsoNormal" style="margin-left:18.0pt"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Best wishes, and I hope this helps to fix the issue,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Ben<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> flash-users-bounces@flash.uchicago.edu <flash-users-bounces@flash.uchicago.edu>
<b>On Behalf Of </b>Xavier Ribeyre<br>
<b>Sent:</b> 14 January 2021 09:33<br>
<b>To:</b> flash-users <flash-users@flash.uchicago.edu><br>
<b>Subject:</b> [FLASH-USERS] Biermann Battery in 2D and 3D geometry<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">Dear
<span class="zmsearchresult">FLASH</span> Code users,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">In the
<span class="zmsearchresult">FLASH</span> version 4.6.2 there is two <span class="zmsearchresult">
Biermann</span> battery test cases. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">One in 2D cartesian geometry and one in 2D axis-symmetric (cylindrical) geometry.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">1-</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"> Whatever in 2D Cartesian or 2D axis-symmetric cases: the magnetic
z component is the same.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">And there is no magnetic field variation whatever I activated the<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">"source BB terms" or the "3T BB term": i.e in flash.par:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">(use_Biermann3T = .false. hy_biermannSource = .true.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">or use_Biermann3T = .true. hy_biermannSource = .false.)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">The z component values of the magnetic field magz are the same.
<strong><span style="font-family:"Arial",sans-serif">This behavior is correct.</span></strong><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">-However it seems that the SIGN of the magz component is not correct in 2D axis-symmetric case (it is the opposite).</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">Are you agree with that?</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">2-
</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">I did the same test case in
<strong><span style="font-family:"Arial",sans-serif">3D geometry</span></strong> with the the same temperature and density profile.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">When I deactivated the source term <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">i.e.
<strong><span style="font-family:"Arial",sans-serif">use_Biermann3T = .true. hy_biermannSource = .false.</span></strong> in the flash.par<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">The values of
<strong><span style="font-family:"Arial",sans-serif">magz</span></strong> seems correct (if we compare with the 2D previous cases)<o:p></o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">BUT</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">When Biermann source term is activated:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">i.e.
<strong><span style="font-family:"Arial",sans-serif">use_Biermann3T = .false.</span></strong>
<strong><span style="font-family:"Arial",sans-serif">hy_biermannSource = .true.</span></strong> in flash.par<o:p></o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">then now the magz values are very different and very low (20 times lower).</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">-I don't know why there is a discrepancy between these two 3D simulations</span></strong><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">I hope you can help to understand what happens.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">Best regards,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black">Xavier Ribeyre<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
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