Feasibility of solving problems with locally field-aligned non-conforming mesh (and more generally what is required for a solver).

[asnodin]

Not sure if a more general issue is needed about what mesh information a solver requires and what type of input it understands (we have so far been passing meshes round as opaque objects without thinking about this too much). I've worked out requirements for most cases with Trixi.

It would be nice to find out if there is any framework that could rapidly deal with the locally field-aligned mesh. Reading the overview of most frameworks one might be convinced that it will just work, since they can do curvilinear, unstructured, hybrid elements, [h|r]-nonconforming, parallel etc. It seems to me that the connectivity information is not supported in most or all cases.

Is there a proof-of-concept that one can study and compare requirements with meshing frameworks and solver?

Discuss.

[cmacmackin]

This paper describes the problem of non-conformal boundaries in Nektar++:
https://www.sciencedirect.com/science/article/pii/S0045782521001560?via%3Dihub

Here are some references to other work on these sorts of methods:

• https://www.sciencedirect.com/science/article/abs/pii/S0021999105004791
• https://www.sciencedirect.com/science/article/abs/pii/S0021999198959563
• https://www.sciencedirect.com/science/article/abs/pii/S0021999112002215
• https://www.sciencedirect.com/science/article/abs/pii/S0021999115002466
• https://www.sciencedirect.com/science/article/abs/pii/S0021999117300281
• https://ntrs.nasa.gov/citations/19890002965
• https://www.sciencedirect.com/science/article/pii/S0045793020303959
• https://www.sciencedirect.com/science/article/pii/S0898122120302029?pes=vor
• https://onlinelibrary.wiley.com/doi/10.1002/nme.394
• https://link.springer.com/article/10.1007/s40314-023-02271-4?fromPaywallRec=true (not a citation of the original paper, but found it under a "related reading section" of one of them)

[jwscook]

NESO-fame exports non-conforming fci finite element meshes for Nektar++. Anisotropic diffusion on these meshes work in some areas of the parameter space. Still more work needed to test.

So far we haven't needed mortaring but have relied on high order integration schemes, which will extend naturally and easily to 3D.