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Hi all,</div>
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I've been having trouble implementing the BSSN equations, as given by CTGamma, in Python using the package COFFEE, which I am very familiar with:</div>
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<a href="https://gitlab.com/thebarista/coffee" id="LPNoLPOWALinkPreview">https://gitlab.com/thebarista/coffee</a><br>
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<a class="doi" href="https://doi.org/10.1016/j.softx.2019.100283" target="_blank" rel="noreferrer noopener" title="Persistent link using digital object identifier" style="box-sizing: border-box; margin: 0px; text-decoration: underline; color: rgb(255, 108, 0); word-break: break-word; font-family: NexusSans, Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 14px;" id="LPNoLPOWALinkPreview_1">https://doi.org/10.1016/j.softx.2019.100283</a><br>
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The main comments are:</div>
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-- For simplicity, I am starting with a 1+1 code (set 2/3 spatial derivatives to be exactly zero).</div>
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-- The 1+log slicing for the lapse and a zero shift.</div>
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-- The "phi" conformal factor type </div>
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-- <span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">The evolution equations are written to Python by a very slight modification of the .m file in CTGEvolution. I've confirmed this .m file outputs the same
file that is in the src directory.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">-- The vanishing of the trace of A is enforced after each full timestep in the same way as CTGamma.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">-- Boundary conditions are not applied.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">-- Fourth order SBP operators that lean over toward the boundaries are used.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">-- Minkowski initial data with all fields zero except \gamma11/22/33.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">-- Euler step is used for time integration to easier compare between Python and the Einstein toolkit.</span></div>
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<span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">This leads to a stable evolution in the Einstein toolkit with the attached .par file using a simple one patch Cartesian grid. However, in Python, I get that
fields diverge, starting at the boundaries and then propagating inward (including with RK4). This behaviour does not go away with higher resolution or reduced CFL. It is however, fixed completely by setting the second spatial derivative of \alpha to be exactly
zero. Trying many different SBP FD operators that have proved successful for other projects has not changed the behaviour. </span></div>
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The COFFEE code has been used and tested in a variety of projects and so there should not be a problem here. Thus, the only thing I can think of, is that the Einstein toolkit is doing something that I am not realizing, that is helping it remain stable. Hopefully,
somebody on this mailing list might have an idea?<br>
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Thanks in advance,</div>
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Chris</div>
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