Sliding mesh-like approach using dealii

[Bruno Blais]

Hello everyone,

As some of you might know, sliding mesh approaches are generally used in CFD simulation of rotating geometries without axial symmetry (for instance, an impeller with baffles).

This is generally achieved by having two triangulation, one that is rotating and one that is static. At the interface between the meshes, constraints are used to "bridge" the two meshes together. Although this generally induces additional interpolation error, this is generally one of the best way to deal with turbomachinery.

Since dealii is already equipped to deal with contact problem, has anybody ever investigated if a sliding-mesh type of simulation could be carried out using dealii?

Thanks

Bruno

[Earl Fairall]

As far as I know, there is no slide mesh function per say; however, deal.ii does have a rotate mesh function which is pretty straightforward to use. Presumably if you apply a cylindrical mesh in the airgap with a known number of uniform segments, you can rotate the mesh by an angle corresponding to the number of segments and the nodes will always match up. In my experience, generating this type of mesh is very difficult from within Deal.ii itself, but presumably you can get this mesh from an external program, I would think it would be straight forward. I am attempting to create a geometry with slide mesh as well.

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[Wolfgang Bangerth]

Bruno,

I don't know, but then there are 1,200+ publications at
https://dealii.org/publications.html
that might contain something you're looking for. There's now even a search
function :-)

There are going to be two challenges:
* Mesh generation. Earl Fairall already commented on that.
* Generation of the constraints. That's going to be difficult because
you'll have to find quadrature points on the faces of one mesh on the
faces of the other mesh, and these sorts of point search algorithms
are always expensive (though easy to parallelize). You need this kind
of mapping if you want to project between the two mesh surfaces; for
interpolation, you'll need to find the location of the support points
of the faces of one mesh on the faces of the other mesh, which is the
same kind of operation.

You could consider a mortar approach in which you would have a third mesh at
the interface. In that case, you could choose at least one of the meshes
involved to be somewhat structured, but in the end, it's probably going to be
about as expensive as otherwise.

I don't know anyone who has implemented the exact kind of application you
have, but you might want to look up some of the work done on fluid-structure
interaction in deal.II (e.g., by Thomas Wick). I *believe* that they too have
to interpolate between different kinds of meshes. There is also the
'nonmatching' namespace that was added by Luca Heltai and coworkers in the
last release that helps you deal with overlay meshes -- which would also be a
way to do what you're looking at -- the rotating geometry would simply be an
overlay to a background mesh. I believe there is also a tutorial program for that.

Other than that, I have no real pointers. But it's an interesting topic, and
if you find ways to implement what you are looking for, please feel free to
post solutions here (and/or make small test programs available as code gallery
or tutorial program!

Best
W.


--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Bruno Blais]

Dear Earl and Wolfgang,

Thanks for the very thorough answer.

I will definitely look into it this year and try to come up with a solution. I think there are many ways to tackle this type of approach using the existing tools :)

I'll keep you informed should I find a way to make a decent implementation.

Best!

Bruno