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<p>Hi Jonas,</p>
<p><br>
</p>
<p>as Dominic points out, we have a NLTPFA implementation in Dumux. I think that this currently is still in a private application module, hosted by Martin Schneider (in cc). But it uses the same technical infrastructure as our publicly available linear MPFA,
a pointer to the class documentation would be at <a href="https://dumux.org/doxygen/master/a01630.html#ga82ff36ab4394ccafc81a0750fca4c69e" class="OWAAutoLink" id="LPlnk879198" previewremoved="true">https://dumux.org/doxygen/master/a01630.html#ga82ff36ab4394ccafc81a0750fca4c69e</a>.
The simplest one-phase incompressible test "<span>test_1p_incompressible_mpfa" can be found at <a href="https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/tree/master/test/porousmediumflow/1p/implicit/incompressible" class="OWAAutoLink" id="LPlnk238446" previewremoved="true">https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/tree/master/test/porousmediumflow/1p/implicit/incompressible</a>.
The discretization is based on the core modules only without involving PDELab.</span></p>
<p><span><br>
</span></p>
<p><span>Kind regards</span></p>
<p><span>Bernd</span></p>
<p><br>
</p>
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<span style="font-family:"Courier New",monospace; font-size:10pt">Bernd Flemisch</span><br>
<span style="font-family:"Courier New",monospace; font-size:10pt">IWS, Universität Stuttgart phone: +49 711 685 69162</span><br>
<span style="font-family:"Courier New",monospace; font-size:10pt">Pfaffenwaldring 61 email: bernd@iws.uni-stuttgart.de</span><br>
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<a href="http://www.iws.uni-stuttgart.de/en/lh2/" class="OWAAutoLink" title="http://www.iws.uni-stuttgart.de/en/lh2/ Ctrl+Klicken oder tippen Sie, um dem Link zu folgen." id="LPNoLP">
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<span style="font-family:"Courier New",monospace; font-size:10pt">_________________________________________________________________</span></div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>Von:</b> dune-pdelab <dune-pdelab-bounces@lists.dune-project.org> im Auftrag von Dominic Kempf <dominic.r.kempf@gmail.com><br>
<b>Gesendet:</b> Montag, 6. Juli 2020 16:41:48<br>
<b>An:</b> Jonas Beddrich<br>
<b>Cc:</b> dune-pdelab@lists.dune-project.org<br>
<b>Betreff:</b> Re: [dune-pdelab] Access to another cell in alpha_skeleton</font>
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<div>Hey Jonas,</div>
<div><br>
</div>
<div>welcome to PDELab! I wished I had a better welcoming gift to you...</div>
<div><br>
</div>
<div>I am assuming that the scheme you are trying to implement is something like Figure 1b from</div>
<div>"Nonlinear two-point flux approximation for modelingfull-tensor effects in subsurface flow simulations"</div>
<div>by Chen et al. - correct me if I am wrong.</div>
<div><br>
</div>
<div>We get this question and variations of it a lot, and unfortunately the most adequate answer is:</div>
<div>The assumption that a facet integral only depends on the two neighboring cells</div>
<div>is built quite deeply into the PDELab assembler. That being said, there is no clean solution to</div>
<div>your problem in PDELab.</div>
<div><br>
</div>
I know that DuMux (<a href="http://www.dumux.org">www.dumux.org</a>, a downstream project) has treated that problem before.
<div>I am not sure they are relying on the PDELab assembler in their implementation, but it is worth</div>
<div>asking them.</div>
<div><br>
</div>
<div>Of course, things can always be hacked. Most probably one can do something with precomputation</div>
<div>of all flux values at all intersection mid points, but I am not sure about the details (e.g. I have no</div>
<div>clues about how jacobians for such a system could be computed).<br>
</div>
<div><br>
</div>
<div>Best,</div>
<div>Dominic<br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Mon, Jul 6, 2020 at 3:30 PM Jonas Beddrich <<a href="mailto:jonas.beddrich@gmail.com">jonas.beddrich@gmail.com</a>> wrote:<br>
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<div>Hi everyone, </div>
<div><br>
</div>
<div>I'm looking for a method to access the values of cells in the alpha_skeleton function of my local operator in addition to the values of the inside and outside cell of the intersection.
<br>
</div>
<div><br>
</div>
<div>The nonlinear Two Point Flux Approximation I'm currently working on requires information about 4 cells to compute the flux through each intersection. So in addition to the inside and outside cell two additional cells m and k are required. The cells m and
k are dependent on the intersection, the inside and outside cell as well as problem parameters. Right now I can determine the index of those cells and then get the corresponding elements by iterating over the grid.
<br>
</div>
<div><br>
</div>
<div>Sadly, I haven't found an efficient way to access the values of these cells, since alpha_skeleton only gets the local vectors and local function spaces of the inside and outside cell. But I guess I'm not the only person encountering this problem. Can anyone
give me a hint on how to solve this? <br>
</div>
<div><br>
</div>
<div>Best regards, <br>
</div>
<div>Jonas <br>
</div>
</div>
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