Instabilities in 1D

[RaphaelPile]

Hello everyone,

I was studying the glow discharge case in 1D and I got these oscillations close to the boundaries (which doesn't seem to exist with the 2D model).

I was wondering if it is something someone here have already encountered or not ?

Thanks for any help.

Raphaël

[markus-m-becker]

Hard to say without knowing which quanity is shown in the figure...a good indicator of the origin of such oscillations is to check if they vanish when refining the mesh. Yes => most probably issue with high Peclét number (mostly on outflow boundaries). No => maybe temporal instability (for explicit integration methods, check with smaller time steps) or implementation error.

[AleksandarJ1984]

Hi Raphaël,

In addition to Markus' comment, I would suggest an interesting article on spurious oscillations that appear when SUPG is used for stabilisation by V John and P Knobloch Comput. Methods Appl. Mech. Engrg. 196 (2007) 2197–2215. They give a thorough review of the methods for preventing boundary layer oscillations. These methods usually require modification of the matrix components, so it is not straightforward for implementation in the present code. Although, it is possible. Have you used stabilisation in your implementation of this example?

Besides that, it is also possible that the oscillations are a form of Gibbs phenomenon (see discussion about similar oscillations here). It could be that the energy of secondary electrons is a bit overestimated, so the transition to the bulk value could cause this phenomenon (which is a bit surprising since they do not appear in the 2D example). You can try to vary the value of the coefficients (i.e. vary the energy of secondary electrons and, if this does not help, secondary electron emission and reflection coefficient) to see if this will improve your result near the boundary.

[RaphaelPile]

@markus-m-becker Yeah sorry the screenshot does not include the quantity. Actually I'm looking at the Ar+ ions, but there are similar issue on all the quantities. Difficult to know who is the cause/consequence. I use the automatic step size, so it should be an issue.

EDIT: "which rapidly get out of the time step range (trying to go to very small values less 1e-30). It gets worse with the mesh refinement." >> Sorry this is an issue on another problem of my own.

The oscillation are concentrated closer to the boundaries when the mesh is refined (but amplitude does not significantly change).

@AleksandarJ1984 I am still using your log stabilization. I have "just" put the glow discharge in 1D. Thanks for the idea, maybe it is because it is not a uniform electron avalanche along the radius in 2D, so the energy of secondary electrons is "damped" somehow by the 2D geometry.