Dear Ankang,
Thank you very much for your kind reply.
I tried the method you suggested, and it worked very well—the issue with the eigenvalue being 1 no longer appears.
However, I still have one question regarding BaseFlow_interporder. Specifically, when performing Floquet stability analysis on a non-periodic base flow, how should the temporal slices be selected? I previously attempted to apply BaseFlow_interporder to such a case, but found that the results varied significantly depending on the choice of the time interval for the slices.
Could you kindly advise on how to handle this issue?
Best regards,
Xiangjun Shan

发件人: ankanggao@ustc.edu.cn <ankanggao@ustc.edu.cn>
发送时间: 2025年4月22日 14:52
收件人: shan xiangjun <x_j_shan@outlook.com>
抄送: Nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk>
主题: Re: [Nektar-users] Questions Regarding Eigenvalue Computation in Stability Analysis
 

Hi Xiangjun,


You can use a smooth initial disturbance to avoid eigenvalue of 1. If BaseFlow_interporder is not zero, the code uses a Lagrange interpolation 

and it can be used for non-periodic baseflow. Additionally, you can select a near body domain to compute the eigenvalue, seting the option SelectEVCalcDomain0, 

since the far-field grids are usually coarse and contains large numerical errors.


We have tested this feature in our previous paper, see appendix

Gao A K, Cantwell C D, Son O, et al. Three-dimensional transition and force characteristics of low-Reynolds-number flows past a plunging airfoil[J]. Journal of Fluid Mechanics, 2023, 973: A43.


Best Regards

Ankang Gao


Research Associate
Department of modern mechanics
University of Science and Technology of China


-----Original Messages-----
From: "shan xiangjun" <x_j_shan@outlook.com>
Send time: Tuesday, 04/22/2025 14:17:20
To: "Sherwin, Spencer J" <s.sherwin@imperial.ac.uk>, "Chris Cantwell" <c.cantwell@imperial.ac.uk>
Cc: "Nektar-users@imperial.ac.uk" <nektar-users@imperial.ac.uk>
Subject: [Nektar-users] Questions Regarding Eigenvalue Computation in Stability Analysis

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Dear  Prof,
I hope this message finds you well.
I am currently conducting a Floquet analysis and using the ModifiedArnoldi method to compute the leading eigenvalues. When the parameter beta is small, the computation converges and produces reasonable results. However, when beta becomes large, all computed maximum eigenvalues turn out to be 1. Increasing the nvec parameter makes it difficult for the calculation to converge. I also tried using the Arpack option and obtained the same results.
Could you  please advise on how to resolve this issue?
Additionally, I would like to inquire about the application scenarios for the BaseFlow_interporder parameter. Can it be used in stability analyses for non-periodic problems?
Thank you very much for your time and support. I look forward to your guidance.
Best regards,
Xiangjun Shan