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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Dear Sean and John,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Thanks for your quick replies!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">In the runs which produced the figures I sent across yesterday I had used these settings<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">E_modification = .true.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">E_upwind = .false.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">energy_fix = .true.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">prol_method = “balsara_prol”<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">with the Roe solver and “order = 2 “ run time parameter.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I’ve since played with these settings and the choice of Riemann solver but unfortunately it looks like this particular artefact might be somewhat different to those seen
in Sean’s loop advection test since it seems to be resilient to these changes.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Specifically, I’ve since tried the following<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoListParagraph" style="margin-left:54.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo1">
<![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><span style="mso-list:Ignore">1)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Enable E_upwind whilst retaining other settings as above.
<br>
There is no appreciable difference.<br>
<br>
<o:p></o:p></span></p>
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</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Changing the prol_method.<br>
<br>
This makes no difference as far as I can tell (not even a slight change in the current amplitudes). I wondered if that in of itself was not strange?<br>
<br>
Is it possible that the that special prolongation is only being applied when a block is refined to a lower level, but not when blocks of different levels of refinement compute guard cell data, but rather only some simple interpolation?<br>
<br>
<o:p></o:p></span></p>
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</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Changing the Riemann solver from Roe to Hybrid to HLLD (reading the manual, Table 14.9 pg 219 makes it sound like these are the only options for USM?)<br>
<br>
There are some slight quantitative differences but overall this doesn’t seem to help remove this particular artefact.<br>
<br>
<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:54.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo1">
<![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><span style="mso-list:Ignore">4)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Changed the runtime parameter “order” from 1,2,3,5 for Roe, Hybrid, and HLLD.<br>
<br>
Orders > 2 showed only slight quantitative differences, with no real effect to supress the artefact.
<br>
<br>
Interestingly, order = 1 does change something. <br>
<br>
For the Roe solver I’ve found that the current artefacts are reduced to singular points in the ‘corners’ of order 1e-15 , but this doesn’t resolve the problem altogether in that there are still artefacts in the flow fields at the refinement region boundaries
(i.e., setting it to 1 seems to not compute bad current, but still sets up the flow fields associated with this artefact).
<br>
<br>
Order =1 for Hybrid and HLLD introduced new class of artefact associated with high eint and v at different locations, and crashed very quickly, “computed dt not positive”.<br>
<br>
<o:p></o:p></span></p>
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</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I’ve checked that this occurs in both ideal MHD and with fairly large resistivity (1e-3). There is some quantitative change due to the diffusion but overall you
still get this wave-launching from the corners.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I did wonder if it might be worth changing NGUARD (thus, how many cells the coarse side of the boundary needs to be interpolated into) but for the life of me I couldn’t figure
out where you actually change this in the code (is it a setup argument? Flash.par didn’t seem to accept it). Can someone please let me know how to do this?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Thanks,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Jonathan<o:p></o:p></span></p>
<p class="MsoNormal"><a name="_MailEndCompose"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></a></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> Sean Couch [mailto:smc@flash.uchicago.edu]
<br>
<b>Sent:</b> 11 May 2016 14:36<br>
<b>To:</b> John ZuHone<br>
<b>Cc:</b> Jonathan Thurgood; flash-users@flash.uchicago.edu<br>
<b>Subject:</b> Re: [FLASH-USERS] MHD (8wave & USM): Refinement region boundaries - spurious waves when B field is oblique to jumps in refinement.<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Good point, John!<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I was using 5th-order WENOZ with HLLD. There is a sort of odd-even-like artifact that can crop up in HLLD. I’ve found a little bit of magnetic resistivity goes a long way toward fixing that. I put together <a href="https://nagini.pa.msu.edu/index.php/s/JpBSEYEOzc4XZT9">a
quick gif</a> of the magnetic pressure from the field loop test I did demonstrating the artifacts I saw and how they depend on the E-field construction parameters/Riemann solver/resistivity.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Sean<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On May 11, 2016, at 8:58 AM, John ZuHone <<a href="mailto:jzuhone@space.mit.edu">jzuhone@space.mit.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">It may also be relevant to know what hydro reconstruction method is being used in the case of USM (for both Sean and Jonathan?). There are known problems of this sort when using HLLD, for example. <o:p></o:p></p>
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<p class="MsoNormal">On May 11, 2016, at 8:56 AM, Sean Couch <<a href="mailto:smc@flash.uchicago.edu">smc@flash.uchicago.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Hi Jonathan,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I’ve seen similar, though not identical, artifacts at refinement boundaries with USM using similar nested AMR grids in the context of stellar core collapse. I was also able to reproduce artifacts using a simple field loop advection test
that traverses a fixed jump in refinement. What I found helped or, in the latter case, completely cleared it up was the following settings:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">E_modification = .true. # High order algorithm for E-field construction <br>
E_upwind = .true. # upwinding for E-field construction <br>
energyFix = .true. # Update magnetic energy using staggered B-fields<o:p></o:p></p>
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<p class="MsoNormal">prolMethod = “injection_prol" # Prolongation method (injecton_prol, balsara_prol) <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I think the last setting in particular is relevant here. This is the method of prolongation in the guardcells at refinement boundaries. What option are you currently using? Injection is the default. You may try switching the prolMethod
and see if that changes anything. <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I’m interested to here if any of this as an effect on what you’re seeing!<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Sean<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><br>
----------------------------------------------------------------------------------------------------------<br>
Sean M. Couch<o:p></o:p></p>
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<p class="MsoNormal">Assistant Professor<br>
Department of Physics and Astronomy<br>
Department of Computational Mathematics, Science, and Engineering<br>
National Superconducting Cyclotron Laboratory/Facility for Rare Isotope Beams<br>
Michigan State University<br>
567 Wilson Rd, 3250 BPS<br>
East Lansing, MI 48824<br>
(517) 884-5035 —— <a href="mailto:couch@pa.msu.edu">couch@pa.msu.edu</a> —— <a href="http://www.pa.msu.edu/~couch">www.pa.msu.edu/~couch</a><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On May 11, 2016, at 7:55 AM, Jonathan Thurgood <<a href="mailto:jonathan.thurgood@northumbria.ac.uk">jonathan.thurgood@northumbria.ac.uk</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Dear All,<span class="apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I was hoping someone might be able help me to overcome a seemingly serious problem which looks like it might prohibit me from migrating my current research project to FLASH.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">SETUP DESCRIPTION:</span></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">The test setup is a linear, 2D magnetic null point:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">B=[x,-y] .<span class="apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">This is a cylindrically symmetric structure where the magnetic field strength linearly increases with radius. It is in force balance between magnetic tension and magnetic
pressure and is known to be a stable equilibrium. All other parameters are taken as constants. I essentially want to study implosions guided into this structure, so have implemented a ‘fixed’ multi-resolution mesh whereby the highest levels of refinement
are clustered towards B=0 at the origin, e.g.:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/fig_fieldlines.png"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/fig_fieldlines.png</span></a>
(2d null point, field line structure)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/nullpoint_modb.png"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/nullpoint_modb.png</span></a><span class="apple-converted-space"> </span> (2d
null point, modB profile and multi-resolution grid overlaid)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/grid_structure.png"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/grid_structure.png</span></a><span class="apple-converted-space"> </span>(grid
structure)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I have implemented this by adding the following lines to Grid_markRefineDerefine.F90, after line 131 but before line 135 (without any other modification).<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">! call Grid_markRefineSpecialized<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> gmrs_size = 4<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> gmrs_spec = (/ 0.0, 0.0, 0.0, 0.01 /)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> call Grid_markRefineSpecialized(INRADIUS, gmrs_size, gmrs_spec, lrefine_max)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I have turned off adaptive refinement by not specifying any refine_vars in flash.par . This is because I am worried about prolongation of a B=0 containing cell causing issues,
so would prefer to set the equilibrium field directly in the initial condition to ensure only one cell contains the null point itself. <i>Please note also that I am worried that it is possible that the problem I am about to describe will be manifest in many
other setups / applications with actual adaptive refinement also, but would be harder to spot.</i><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">PROBLEM DESCRIPTION / FIGURES:</span></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">If I then run the code to test the stability of the equilibrium (ie., no perturbations), the following current pattern quickly builds up at the boundaries of each refinement
level. This then launches inward-propagating waves towards the origin/null point, at large enough amplitudes to interfere with the solution.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order2.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order2.gif</span></a><span class="apple-converted-space"> </span>(CurZ,
USM, monotonic, interpolation order 2)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I believe this problem is to do with the guard cell filling by interpolation on the refinement boundary calculating an inappropriate field value which specifies a bogus
current and launches waves driven by this erroneous imbalance of Lorentz force. This seems to be particularly bad in the corners here where the field strength is increasing obliquely to the cell faces, and so we have the impression of wave fronts emanating
predominantly from the corners of the refinement boundaries.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Changing the monotonic interpolation order for guard cell filling, or switching to 8 wave with PARAMESH’s native interpolation, unfortunately does not fix this, but does
change the shape and size of the artefacts as follows<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order0.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order0.gif</span></a><span class="apple-converted-space"> </span>(curz,
USM, monotonic, interpolation order 0)<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order1.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order1.gif</span></a><span class="apple-converted-space"> </span>(curz,
USM, monotonic, interpolation order 1)<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order2.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_usm_monotonic_order2.gif</span></a><span class="apple-converted-space"> </span>(curz,
USM, monotonic, interpolation order 2)<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_8wave_native.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_8wave_native.gif</span></a><span class="apple-converted-space"> </span> (curz,
8wave,native)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">It is also interesting to note that I have in the past encountered a similar qualitative current build up / wave launching from the external/physical boundary if I use, say,
outflow boundary conditions (or any other default) at the null, rather than my user defined condition which explicitly sets the field in the boundary.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_uniformgrid_defaultbc.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_uniformgrid_defaultbc.gif</span></a><span class="apple-converted-space"> </span> (curz,
USM, outflow boundary + uniform)<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/current_uniformgrid_userbc.gif"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/current_uniformgrid_userbc.gif</span></a> (curz,
USM, user defined boundary + uniform grid)<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">(note, by uniform grid I mean that these runs just set minimum and maximum refinement level to be the same, rather than switching to UG mode properly)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">You can see that any current for the correct BC is just numerical noise (note the magnitude), whereas the default boundary conditions give similar behaviour to that noticed
at the refinement boundaries. I think this supports the idea that field is not correctly calculated at the boundaries of refinement (in the case of using outflow boundary at a null, field is incorrectly specified by the BC, in the case of refinement region
boundaries, field is incorrectly specified by interpolation.)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">OTHER SETUPS THAT SEEM TO HAVE THE SAME PROBELM</span></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">I can also reproduce the problem in another geometry suggesting that it isn’t specific or unique my 2D null point.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">For example, I’ve tried the one dimensional field used in the Taylor problem and other reconnection studies. Here, if<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">B = [0,x] + pressure chosen to maintain force balance<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/taylor_problem_modb.png"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/taylor_problem_modb.png</span></a><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> (see also<span class="apple-converted-space"> </span><a href="http://adsabs.harvard.edu/abs/2003PhPl...10.4284F"><span style="color:purple">http://adsabs.harvard.edu/abs/2003PhPl...10.4284F</span></a><span class="apple-converted-space"> </span>,
which considered this problem with an early version of FLASH)<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">is considered with the same sort of static, multi-level grid I used at the null no such problems are initially encountered.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">However, if one rotates everything by 45degrees so that the gradients in magnetic field are now oblique to the Cartesian grid, e.g.,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><a href="https://jonathanthurgood.files.wordpress.com/2016/05/taylor_problem_rotated_modb.png"><span style="color:purple">https://jonathanthurgood.files.wordpress.com/2016/05/taylor_problem_rotated_modb.png</span></a><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">similar artefacts to those described above for the null point can be clearly seen at the refinement boundaries.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Although I think I have the gist of why this is happening, I’m not sure about how to narrow it down further or begin to correct it. Any advice on any aspect of the above,
how to narrow this down further, possible solutions or general advice would be very much appreciated – I am very stuck!<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Thanks for reading.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Best regards,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif"">Jonathan<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"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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