<div dir="ltr"><div dir="ltr">On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <<a href="mailto:bldenton@buffalo.edu">bldenton@buffalo.edu</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg-5863090716063271256">
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Thank you for the discussion.</div>
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Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions?</div></div></div></blockquote><div><br></div><div>I am not sure what natural coordinates are. Do we just mean the Jacobian, derivatives of the map between reference and real coordinates? If so, yes the Jacobian is available. Right now I do not pass it</div><div>directly, but passing it is easy.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg-5863090716063271256"><div dir="ltr">
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Matt - Thank you for the command line option for the 2<span><sup>nd</sup> derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference
for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference.</span></div>
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<span>Jed - Thank you for the link. I will review the information on it. </span></div>
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<span style="background-color:rgb(255,255,255);display:inline">Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here).</span><br>
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<div id="m_-5863090716063271256divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Jed Brown <<a href="mailto:jed@jedbrown.org" target="_blank">jed@jedbrown.org</a>><br>
<b>Sent:</b> Wednesday, October 11, 2023 1:38 PM<br>
<b>To:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Cc:</b> Brandon Denton <<a href="mailto:bldenton@buffalo.edu" target="_blank">bldenton@buffalo.edu</a>>; petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization</font>
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<div>Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> writes:<br>
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> On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <<a href="mailto:jed@jedbrown.org" target="_blank">jed@jedbrown.org</a>> wrote:<br>
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>> I don't see an attachment, but his thesis used conservative variables and<br>
>> defined an effective length scale in a way that seemed to assume constant<br>
>> shape function gradients. I'm not aware of systematic literature comparing<br>
>> the covariant and contravariant length measures on anisotropic meshes, but<br>
>> I believe most people working in the Shakib/Hughes approach use the<br>
>> covariant measure. Our docs have a brief discussion of this choice.<br>
>><br>
>> <a href="https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet" target="_blank">https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flibceed.org%2Fen%2Flatest%2Fexamples%2Ffluids%2F%23equation-eq-peclet&data=05%7C01%7Cbldenton%40buffalo.edu%7Cd9372f934b26455371a708dbca80dc8e%7C96464a8af8ed40b199e25f6b50a20250%7C0%7C0%7C638326427028053956%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=skMsKDmpBxiaXtBSqhsyckvVpTOkGqDsNJIYo22Ywps%3D&reserved=0</a><br>
>><br>
>> Matt, I don't understand how the second derivative comes into play as a<br>
>> length measure on anistropic meshes -- the second derivatives can be<br>
>> uniformly zero and yet you still need a length measure.<br>
>><br>
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> I was talking about the usual SUPG where we just penalize the true residual.<br>
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I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative
of reference coordinates with respect to physical (or equivalently, the associated metric tensor).<br>
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</div></blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>