<div dir="ltr">One quick clarification:<div><br></div><div>When I said</div><div>> "[integrated measures of rest mass over a volume] can become completely unreliable at the time of black hole formation"</div><div><br></div><div>I meant that the conservative nature of GRMHD schemes can and do break down inside black holes, so mass might be lost after it passes inside a black hole horizon. This should have no ill effect outside the horizon, as "what happens in the horizon stays in the horizon". Generally you'd want to perform a surface integral to monitor the rest mass passing into the horizon and combine it with a volume integral outside the horizon to measure the total rest mass after black hole formation.</div><div><br clear="all"><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px">-Zach</div><div style="font-size:12.8px"><br></div><span style="font-size:12.8px">* * *</span><br style="font-size:12.8px"><span style="font-size:12.8px">Prof. Zachariah Etienne</span></div><div dir="ltr">Physics & Astronomy Dept.<br style="font-size:12.8px"><div style="font-size:12.8px">West Virginia University</div><div><a href="http://astro.phys.wvu.edu/zetienne/" target="_blank">http://astro.phys.wvu.edu/zetienne/</a></div><div><a href="http://blackholesathome.net/" target="_blank">http://blackholesathome.net</a><a href="https://blackholesathome.net" style="font-size:12.8px" target="_blank"><br></a><br></div></div></div></div></div></div></div></div></div></div></div></div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Feb 12, 2020 at 11:05 PM Zach Etienne <<a href="mailto:zachetie@gmail.com">zachetie@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Hi ZhiChao,<div><br></div><div>> The program runs without error, however there is no eject during the merge. </div><div><br></div><div>Typical ejecta from BNS mergers amount to a very tiny fraction of the total initial mass, with values of 1e-3 Msun from BNS merger simulations being reported in the literature (<a href="https://arxiv.org/abs/1809.11161" target="_blank">https://arxiv.org/abs/1809.11161</a>). This value is highly dependent on the equation of state however. Further most simulations reporting ejecta are not performed at multiple numerical resolutions, meaning that the values may be adjusted downwards with subsequent simulations. Indeed in most simulations I saw for which more than one resolution was performed in that paper, the higher resolution simulation has less ejecta (see Table 2)--sometimes significantly less (e.g., LS220_M140140_LK).</div><div><br></div><div>Bottom line, I am not surprised you didn't see any ejecta. Ejecta measurements are often dominated by numerical error, and depend sensitively on equation of state. The very simple equation of state you chose (simple Gamma=2 polytrope) might not exhibit much, if any, ejecta in the limit of very high resolution. </div><div><br></div><div>A recent update to IllinoisGRMHD supports more sophisticated (piecewise polytrope/"hybrid") equations of state. It exists within the IllinoisGRMHD subdirectory of <a href="https://github.com/zachetienne/nrpytutorial" target="_blank">https://github.com/zachetienne/nrpytutorial</a> . You might have more luck getting ejecta from BNS initial data with piecewise-polytrope equations of state.</div><div><br></div><div>> And "restmass. Init. IN sphere @ (0.000000e+00,0.000000e+00,0.000000e+00), r=2.708902e+02. Moves/Tracks AMR Centre -1/-1" is increasing.</div><div><br></div><div>If I'm interpreting this correctly (I might not be), you are measuring total rest mass within 270.89 in code units. You seem to observe an increase of 0.06% over the course of the simulation. That's not much, and can happen due to interpolation errors at AMR refinement boundaries (matter crosses AMR refinement boundaries and tiny errors add up to a small boost in mass), or become completely unreliable at the time of black hole formation. Performing another simulation at higher or lower resolution and additional volume integral regions may help diagnose this measurement. I think you'd want to analyze the rest mass *outside* an interior volume to estimate ejecta anyway. </div><div><br></div><div>A more sophisticated interpolation treatment at AMR refinement boundaries might help reduce this error, which amounts to a different prolongation type (e.g., ENO) being chosen for evolved GRMHD variables.</div><div><br></div><div>Hope this helps.</div><div><br clear="all"><div><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px">-Zach</div><div style="font-size:12.8px"><br></div><span style="font-size:12.8px">* * *</span><br style="font-size:12.8px"><span style="font-size:12.8px">Prof. Zachariah Etienne</span></div><div dir="ltr">Physics & Astronomy Dept.<br style="font-size:12.8px"><div style="font-size:12.8px">West Virginia University</div><div><a href="http://astro.phys.wvu.edu/zetienne/" target="_blank">http://astro.phys.wvu.edu/zetienne/</a></div><div><a href="http://blackholesathome.net/" target="_blank">http://blackholesathome.net</a><a href="https://blackholesathome.net" style="font-size:12.8px" target="_blank"><br></a><br></div></div></div></div></div></div></div></div></div></div></div></div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Feb 12, 2020 at 9:25 PM ZhiChao Zhao <<a href="mailto:yanyuechuixue@gmail.com" target="_blank">yanyuechuixue@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Hello everyone,<div><br></div><div>I am Zhi-Chao Zhao from Beijing Normal University, China.</div><div>I am using EinsteinToolkit and IllinoisGRMHD to simulate BNS merge.</div><div><br></div><div>I use a par file modified from <a href="https://bitbucket.org/zach_etienne/wvuthorns_diagnostics/src/master/NSNS_parameter_files/nsns_test.par" target="_blank">https://bitbucket.org/zach_etienne/wvuthorns_diagnostics/src/master/NSNS_parameter_files/nsns_test.par</a> .</div><div>I just add one line "VolumeIntegrals_GRMHD::volintegral_inside_sphere__radius[6] = 270.89015422746235".</div><div><br></div><div>The initial data is got from Zach Etienne.</div><div><br></div><div>The program runs without error, however there is no eject during the merge. </div><div>Two videos:</div><div><a href="https://gogo.treenew.be/rho_b_movie.mpg" target="_blank">https://gogo.treenew.be/rho_b_movie.mpg</a><br></div><div><a href="https://gogo.treenew.be/rho_b_log_movie.mpg" target="_blank">https://gogo.treenew.be/rho_b_log_movie.mpg</a><br></div><div><br></div><div><br></div><div>And "restmass. Init. IN sphere @ (0.000000e+00,0.000000e+00,0.000000e+00), r=2.708902e+02. Moves/Tracks AMR Centre -1/-1" is increasing.</div><div>One figure:</div><div><div><a href="https://gogo.treenew.be/newplot.png" target="_blank">https://gogo.treenew.be/newplot.png</a></div></div><div><br></div><div>I don't know where I went wrong. Can anyone help me?<br><br></div><div><br></div></div>
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