Poisson solver and "BC" across dielectric media.

[photon960]

Hi Elmer forum.
My name is Roberto and I am new on elmer (and FEM!).
I am interested to work on multiphysics model that include: Navier-stokes, Poisson, and advection-diffusion equations.
Right now I am working on the Navier-stock equation and I think all is OK. The next step is work on Poisson equation, but there are some things that I can not implement, that is the "boundary" conditions across dielectric media:
Suppose we have a square box, three of its walls are at zero potential and the potential remaining 1V. The box is filled with two dielectric media of dielectric constant \epsilon_1 and \epsilon_2 (the space above the diagonal with medium 1 and the space below the diagonal with medium 2, for example).
How I can implement the continuity conditions of the on the transverse electric field and on the normal electric induction field across the boundary of the media? (E_{t1}=E_{t2} and D_{n1}=D_{n2})

I found at the Elmer site an example (in cylindrical coordinates) but no more information about how to implement can be see.

Someone has worked on the issue? Is there any tutorial that covers how to work with the continuity conditions of the fields on the border of two dielectrics?

Thanks in advance.
Roberto

[raback]

Hi Roberto

You should decleare two different bodies so that you can assign them different material parameters. Other than that I don't think you have to do anything as the continuity of the flux over the boundary is always maintained (in a weak sense).

If your box is exactly as you describe and the material interface is at the diagonal then Delaunay triangularization provided by gmsh or netgen plug-in (in2d format) might provide the most suitable meshing tools. Structured meshing with such a interface is somewhat troublesome .

BR, Peter

[photon960]

Thanks Peter for your information,
I am working on the analitic solution to the problem I presented, and I will compare it whith the elmer solution. After that, I will comment in the forum what I found.
Roberto.

[nino]

Dear Peter
I am trying to solve a 2D electrostatic problem in presence of two dielectric media with Elmer and I have the same problem of Roberto about the boundary condition between different media. My region is circular and I would like to estimate the capacitance matrix of 8 segmented electrodes along a circumference which is inside this region. The part of the region between electrodes is partially filled with a medium with water (M1) while the rest is air (M2), changing the shape of M1 the system clearly has no symmetry. I defined only two bodies (for M1 and M2) as you suggested. At the boundary between the two media I am expecting to see some discontinuity of the field but the results seems without any discontinuity.
What do you suggest? Is it possible to implement the boundary condition mentioned by Roberto?
Many thank for the help and for the great work you and your colleagues are doing for the Elmer software
Best regards
Nino

[nino]

Dear Peter
any time I load the project the boundary conditions are lost, and this is annoying especially with many boundary lines, therefore
I found a problem in the sif file (the medium was not set properly) and now the field show a discontinous behavior, so forget my previous message.
best regards
Nino

[raback]

Hi Nino

The missing activation in project loading should be repaired since 1st of March.

The visualization of discontinuous fields is sometimes problematic. For example, the electric potential is a continuous quantity whereas the electric flux density has discontinuities. The mesh has, however, just one set of nodes at the interface so the visualization software cannot present the discontinuous fields properly. The visualization improves of course with mesh density.

-Peter