[evgenii]

Hi, people!

I wrote my own solver to solve electromagnetic problems. This program solves set of curl Maxwell equations. and now I am testing it solving problems for resonators. I used it for quite complicated geometry as cross-like volume, it works fine even for quite coarse mesh.

Then I decided to test it for cylindrical geometry, but I failed. I got really unstructured mesh and for this mesh solution exponentionally grows to infinity. Everything that I changed is structured ortogonal mesh to unstructured non-ortogonal mesh.

Could anyone give me advice or any assumption how this problem can be solved?

Thank in advance.
Efimenko Evgeny

[dmoroian]

If by "really unstructured" you ment stretched, then this could be the problem.
Try running checkMesh first to see the quality of your mesh.

Dragos

[evgenii]

Thank you for advise! But I am not common with this utility. Can you tell me something about following output?

Checking geometry...
Boundary openness in x-direction = 4.78574e-20
Boundary openness in y-direction = -3.1552e-20
Boundary openness in z-direction = 2.21605e-18
Boundary closed (OK).
Max cell openness = 6.35275e-22 Max aspect ratio = 1.0484. All cells OK.

Minumum face area = 3.08352e-07. Maximum face area = 1.81143e-06. Face area magnitudes OK.

Min volume = 3.22811e-10. Max volume = 1.72756e-09. Total volume = 5.02447e-05. Cell volumes OK.

Mesh non-orthogonality Max: 19.1576 average: 3.7965
Non-orthogonality check OK.

Face pyramids OK.

Max skewness = 24.4986 percent. Face skewness OK.

Minumum edge length = 0.000486087. Maximum edge length = 0.00151374.

All angles in faces are convex or less than 10 degrees concave.

Face flatness (1 = flat, 0 = butterfly) : average = 0.999998 min = 0.998494
All faces are flat in that the ratio between projected and actual area is > 0.8

Geometry check done.


Regards,
Efimenko Evgeny

[dmoroian]

Well, it basically says that your mesh is good. That means your choice of discretisation is probably not adequate.
I am not familiar with Maxwell equations (the curl form). Are they parabolic or hyperbolic, linear or nonlinear?
State your discretisation schemes for the different terms. Also, what solvers are set for different variables? (system/fvSchemes, system/fvSolution)

Dragos

[olwi]

A simple discretisation that works fine on cartesian grids will fail badly on non-structured grids. I have worked only with liquid-metal MHD, which is easier than the full Maxwell's. Already then you need to make sure you conserve a lot of things. You may for example have to compute certain terms on the faces, to assure that face fluxes are conservative. Then cell centre values can be reconstructed from face fluxes (there's a reconstruct method for that). It's not trivial, and I think you would probably have to skim the literature for algorithms.

If your new geometry is cylinder symmetric, however, you can still make an orthogonal grid in cylindrical coordinates... Maybe your simple discretization might be enough then.

/Ola

[evgenii]

Hi, all!

Thanks greatly for your replies!
You are absolutely right, Ola, I found in one paper (Edelvik, F. 2002. Hybrid Solvers for the Maxwell Equations in Time-Domain. Acta
Univ. Ups. Uppsala Dissertations from the Faculty of Science and Technology) that it is near to impossible to construct a non orthogonal mesh for which FVTD solver for Maxwell equations will be stable. ( It can be, but there's no guarantee that it will in each case). Different technics can be used, but they also do not guarantee that solver will be stable. So it is non-trivial problem to solve.

Thank you for cooperation,
Efimenko Evgeny