[dune-pdelab] Access to another cell in alpha_skeleton

[Flemisch, Bernd]

Hi Jonas,


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 https://dumux.org/doxygen/master/a01630.html#ga82ff36ab4394ccafc81a0750fca4c69e. The simplest one-phase incompressible test "test_1p_incompressible_mpfa" can be found at https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/tree/master/test/porousmediumflow/1p/implicit/incompressible. The discretization is based on the core modules only without involving PDELab.


Kind regards

Bernd


--
_________________________________________________________________

Bernd Flemisch
IWS, Universität Stuttgart               phone: +49 711 685 69162
Pfaffenwaldring 61              email: bernd at iws.uni-stuttgart.de
D-70569 Stuttgart           url: www.iws.uni-stuttgart.de/en/lh2/<http://www.iws.uni-stuttgart.de/en/lh2/>
_________________________________________________________________
________________________________
Von: dune-pdelab <dune-pdelab-bounces at lists.dune-project.org> im Auftrag von Dominic Kempf <dominic.r.kempf at gmail.com>
Gesendet: Montag, 6. Juli 2020 16:41:48
An: Jonas Beddrich
Cc: dune-pdelab at lists.dune-project.org
Betreff: Re: [dune-pdelab] Access to another cell in alpha_skeleton

Hey Jonas,

welcome to PDELab! I wished I had a better welcoming gift to you...

I am assuming that the scheme you are trying to implement is something like Figure 1b from
"Nonlinear two-point flux approximation for modelingfull-tensor effects in subsurface flow simulations"
by Chen et al. - correct me if I am wrong.

We get this question and variations of it a lot, and unfortunately the most adequate answer is:
The assumption that a facet integral only depends on the two neighboring cells
is built quite deeply into the PDELab assembler. That being said, there is no clean solution to
your problem in PDELab.

I know that DuMux (www.dumux.org<http://www.dumux.org>, a downstream project) has treated that problem before.
I am not sure they are relying on the PDELab assembler in their implementation, but it is worth
asking them.

Of course, things can always be hacked. Most probably one can do something with precomputation
of all flux values at all intersection mid points, but I am not sure about the details (e.g. I have no
clues about how jacobians for such a system could be computed).

Best,
Dominic

On Mon, Jul 6, 2020 at 3:30 PM Jonas Beddrich <jonas.beddrich at gmail.com<mailto:jonas.beddrich at gmail.com>> wrote:
Hi everyone,

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.

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.

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?

Best regards,
Jonas
_______________________________________________
dune-pdelab mailing list
dune-pdelab at lists.dune-project.org<mailto:dune-pdelab at lists.dune-project.org>
https://lists.dune-project.org/mailman/listinfo/dune-pdelab
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.dune-project.org/pipermail/dune-pdelab/attachments/20200706/9b5cd2ee/attachment.htm>