MHD setup in Dedalus2

[Erin E Goldstraw]

Dear Dedalus Users,

I am trying to solve the MHD equations. 

The equations and boundary conditions are given in Equation_Summary.pdf. 

My current code setup is given in solar-fmhd-d2_minimal.py. 

Could someone please check this set up? 

I am not sure about the gauge conditions and keep encountering problems with numeric instabilities when running this code. 

Any advice would be greatly appreciate. I would like to understand the Dedalus methodology better.

Please and thank you,

Erin Goldstraw

[Sadokat Malikova]

Dear Erin Goldstraw,

From a quick glance, you are imposing perfectly conducting wall condition:
∂zBx = 0, ∂zBy = 0, Bz = 0.

In your code try with:

 bz=0  bc. 

I think this is the problem.

with best regards,

Sadokat

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[Erin E Goldstraw]

Dear Sadokat,

Thank you for your suggestion. 

I think I have previously tried both d/dz(bz)=0 and bz=0 at one time or another without much affect. 

I will try again. 

Any other suggestions are welcome.

Thank you,

Erin

[Erin E Goldstraw]

Dear Dedalus group,

Thank you for the suggestion. Setting the boundary conditions for Bz to be the derivative of Bz=0 does allow the code to run at least for a couple of hours. I haven't run it longer yet. 

Here are a couple more questions.

Is it possible to use the ideal induction equation for Bz on the boundary? How would this be written?

This code runs at the moment using a maximum timestep of 1e-4. Increasing this to 1e-3 results in infinite kinetic energy before long. 

Any suggestions and advice to improve the stability of this code and in general would be appreciated. In theory I plan to run these simulations for around a simulation time of 400. So a timestep of 1e-4 is going to take a while. 

Thank you again,

Erin Goldstraw

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Dr Erin E. Goldstraw