inquiry about getting the eigenfunction of EVP in dedalus v2

[Yin Wang]

Dear dedalus experts,

I am a beginner of dedalus and am currently using dedalus v2.

My colleague wrote a script based on dedalus v2 to use EVP solver to calculate the maximum growth rate of magnetorotational instability in Taylor-Couette flow. I have attached the script in this thread.

The script runs well on my PC, and I get the maximum growth rate. Now my goal is to get the eigenfunctions of velocity and magnetic fields corresponding to the maximum growth rate. I am wondering if someone could let me know how can I realize this? Or if there is already a thread with the similar issue, please let me know.

Thank you very much!

Best,

Yin

[Daniel Lecoanet]

Hi,

You want to use the solver.set_state() method: https://github.com/DedalusProject/dedalus/blob/v2_master/dedalus/core/solvers.py#L190

It will put the eigenvector data into solver.state, so that you can access the velocity, magnetic field, etc. associated with each eigenmode.

Daniel

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<mri_test.py>

[Jeffrey S. Oishi]

Hi,

Also, please see eigentools: https://github.com/DedalusProject/eigentools

which provides additional support for eigenvalue problems in d2.

Jeff

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[Yin Wang]

Hi Daniel and Jeff,

Thank you both for the information and now I feel like I can use the "solver.set_state() method" to get the "eigenfunctions" of magnetic field and velocity field.

However, these "eigenfunctions" are still a little strange: for a given paramter set, no matter how large the Nr is ( Nr is the number of the Chebyshev grid points in radial direction), only the first 20 data points of each "eigenfunction" are finite (and they don't change with Nr), and all the rest data points are negligibly small.

This makes me feel like these "eigenfunctions" are in the "spectral coordinate" rather than in the "Chebyshev grid coordinate". Could you please confirm this? If this is the case, how can I convert these "spectral eigenfunction coffeecients" to "grid eigenfunction coefficients"?

I also attached my dedalus v2 script to get the  "eigenfunction" for your reference. In my code, at line101 I use "np.argmax" to find the index "ifast" of the eigenmode that has the largest growth rate. Then at line102 I use "solver.set_state(index=ifast)" to locate the corresponding "eigenfunctions". Here I assume that the fastest growing mode's indices in "solver.eigenvalues" and "solver.set_state" are the same, please also help confrim this.

Thank you in advance!

Best,

Yin

[Adrian Fraser]

Hi Yin,

I think you're correct that you're pulling the spectral coefficients. Take a look at input cell 8 here (just before the "Analysis" section), and see how u is set to solver.state['u'] and then you can specifically access u['g'] rather than u['c']. You might try something similar rather than how you are currently accessing these fields in your max_growth_rate function.

The eigenvalue/mode order is the same, yes. But just to reiterate Jeff's point: you should check out Eigentools because it has some quite helpful tools for exactly the things you're trying to do here.

Adrian

[Yin Wang]

Hi Adrian (and all),

Thanks for the information.

Now I can export the "grid coefficients" of the eigenfunction correctly, just by changing "solver.state['ur'].data" to "solver.state['ur']['g'].data" in my script.

My problem is solved, thanks a lot.

Best,

Yin

[Luis]

Hi Adrian and all,

We are working on transfering our MRI code from dedalus v2 to v3. While I was working on the diskbasis, I don't know how to implement boundary conditions at two different radius. For example, we want to have non-slip boundary condition at both r = 1 and r =3. I wonder based on pipeflow script do you have any thought on how to implement these boundary conditions? Thank you!

Best

Hongke

[Jeffrey S. Oishi]

Hi Hongke,

You want AnnulusBasis, not DiskBasis.

Jeff

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[Luis]

Hi Professor Oishi,

Ahhh, I see. Thank you!

Hongke

[Luis]

Hi all,

I implemeneted a annulus flow using AnnulusBasis, but I have a new problem on solving the axissymmetric mode. And the error message is Non-square system: group=(0, None), I=259, J=260. I went back to the pipeflow script and I found the pipeflow script have the same problem if I change sp = solver.subproblems_by_group[(m, None)]  to sp = solver.subproblems_by_group[(0, None)].I wonder if I want to solve for the axissymetric mode then what should I change in terms of tau terms or something else. 

Best

Hongke

On Tuesday, June 25, 2024 at 2:36:16 PM UTC-4 jso...@gmail.com wrote: