Questions Regarding Eigenvalue Computation in Stability Analysis
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* 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
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 | This email from x_j_shan@outlook.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list to disable email stamping for this address. | 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
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 This email from x_j_shan@outlook.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. 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
Hi Xiangjun, Floquet stability only applies to periodic base flows. The non-periodic baseflow is for transient growth analysis. The transient growth rate does depend on the time interval selected, this phenomenon is physical. Best Ankang -----Original Messages----- From:"shan xiangjun" <x_j_shan@outlook.com> Send time:Wednesday, 04/23/2025 10:16:05 To: "ankanggao@ustc.edu.cn" <ankanggao@ustc.edu.cn> Cc: "Nektar-users@imperial.ac.uk" <nektar-users@imperial.ac.uk> Subject: [Nektar-users] 回复: Questions Regarding Eigenvalue Computation in Stability Analysis 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 | This email from x_j_shan@outlook.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list to disable email stamping for this address. | 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
Dear Ankang, I understand now. Thank you very much for your helpful response! Best regards, Xiangjun Shan ________________________________ 发件人: ankanggao@ustc.edu.cn <ankanggao@ustc.edu.cn> 发送时间: 2025年4月23日 10:59 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] 回复: Questions Regarding Eigenvalue Computation in Stability Analysis Hi Xiangjun, Floquet stability only applies to periodic base flows. The non-periodic baseflow is for transient growth analysis. The transient growth rate does depend on the time interval selected, this phenomenon is physical. Best Ankang -----Original Messages----- From: "shan xiangjun" <x_j_shan@outlook.com> Send time: Wednesday, 04/23/2025 10:16:05 To: "ankanggao@ustc.edu.cn" <ankanggao@ustc.edu.cn> Cc: "Nektar-users@imperial.ac.uk" <nektar-users@imperial.ac.uk> Subject: [Nektar-users] 回复: Questions Regarding Eigenvalue Computation in Stability Analysis 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 This email from x_j_shan@outlook.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. 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
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* Dear Ankang, Recently I encountered a similiar issue that when I computed the stability of a naturally steady cylinder flow, the solover always returned a 0 eigenvalue (-1e-10 + i*0) and took much longer time to converge. Inspired by your advice, I tried adding the entry SelectEVCalcDomain0 to restrict the eigenvalue calculation to the region near the cylinder locating at (0, 5). I am expecting to compute the zone from corner (-5, -5) to (10,10), does the entry setting correct? <FUNCTION NAME="SelectEVCalcDomain0"> <E VAR="C0" VALUE="-5" /> <E VAR="C1" VALUE="10." /> <E VAR="C2" VALUE=" -5" /> <E VAR="C3" VALUE="10" /> </FUNCTION> When I used ModifiedArnoldi scheme, the running gives CFL=0 and crashed. When I switched to Arpack option, the calculation ran but the setup kept dumping out zero eigenvalue. Is there any approach that could help improve the simulation? thanks! regards, Wei
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
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
Hi Wei, The domain defined by the SelectEVCalcDomain0 is {(x,y) | C0>0 && C1>0 && C2>0 && ... }. In your case, it should be <FUNCTION NAME="SelectEVCalcDomain0"> <E VAR="C0" VALUE="x+5" /> <E VAR="C1" VALUE="y+10." /> <E VAR="C2" VALUE=" 5-x" /> <E VAR="C3" VALUE="10-y" /> </FUNCTION> You can also define more than 1 domains, the final domain is the union of them, SelectEVCalcDomain0 + SelectEVCalcDomain1 + SelectEVCalcDomain2 + ... Hope it works in your case. Best Ankang -----Original Messages----- From:"Wei He" <weiyh.he@gmail.com> Send time:Tuesday, 04/29/2025 16:53:15 To: "ankanggao@ustc.edu.cn" <ankanggao@ustc.edu.cn> Cc: nektar-users <nektar-users@imperial.ac.uk> Subject: Re: [Nektar-users] 回复: 回复: Questions Regarding Eigenvalue Computation in Stability Analysis | This email from weiyh.he@gmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list to disable email stamping for this address. | Dear Ankang, Recently I encountered a similiar issue that when I computed the stability of a naturally steady cylinder flow, the solover always returned a 0 eigenvalue (-1e-10 + i*0) and took much longer time to converge. Inspired by your advice, I tried adding the entry SelectEVCalcDomain0 to restrict the eigenvalue calculation to the region near the cylinder locating at (0, 5). I am expecting to compute the zone from corner (-5, -5) to (10,10), does the entry setting correct? <FUNCTIONNAME="SelectEVCalcDomain0"><EVAR="C0"VALUE="-5"/><EVAR="C1"VALUE="10."/><EVAR="C2"VALUE=" -5"/><EVAR="C3"VALUE="10"/></FUNCTION> When I used ModifiedArnoldi scheme, the running gives CFL=0 and crashed. When I switched to Arpack option, the calculation ran but the setup kept dumping out zero eigenvalue. Is there any approach that could help improve the simulation? thanks! regards, Wei 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 _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
Hi Ankang, Following your setup, the simulation is running now. Thank you very much! regards, Wei On Tue, Apr 29, 2025 at 6:32 PM <ankanggao@ustc.edu.cn> wrote:
Hi Wei,
The domain defined by the SelectEVCalcDomain0 is {(x,y) | C0>0 && C1>0 && C2>0 && ... }. In your case, it should be
<FUNCTION NAME="SelectEVCalcDomain0">
<E VAR="C0" VALUE="x+5" />
<E VAR="C1" VALUE="y+10." />
<E VAR="C2" VALUE=" 5-x" />
<E VAR="C3" VALUE="10-y" />
</FUNCTION>
You can also define more than 1 domains, the final domain is the union of them, SelectEVCalcDomain0 + SelectEVCalcDomain1 + SelectEVCalcDomain2 + ...
Hope it works in your case.
Best
Ankang
-----Original Messages----- *From:* "Wei He" <weiyh.he@gmail.com> *Send time:* Tuesday, 04/29/2025 16:53:15 *To:* "ankanggao@ustc.edu.cn" <ankanggao@ustc.edu.cn> *Cc:* nektar-users <nektar-users@imperial.ac.uk> *Subject:* Re: [Nektar-users] 回复: 回复: Questions Regarding Eigenvalue Computation in Stability Analysis
This email from weiyh.he@gmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list <https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address.
Dear Ankang,
Recently I encountered a similiar issue that when I computed the stability of a naturally steady cylinder flow, the solover always returned a 0 eigenvalue (-1e-10 + i*0) and took much longer time to converge. Inspired by your advice, I tried adding the entry SelectEVCalcDomain0 to restrict the eigenvalue calculation to the region near the cylinder locating at (0, 5). I am expecting to compute the zone from corner (-5, -5) to (10,10), does the entry setting correct?
<FUNCTION NAME="SelectEVCalcDomain0"> <E VAR="C0" VALUE="-5" /> <E VAR="C1" VALUE="10." /> <E VAR="C2" VALUE=" -5" /> <E VAR="C3" VALUE="10" /> </FUNCTION>
When I used ModifiedArnoldi scheme, the running gives CFL=0 and crashed. When I switched to Arpack option, the calculation ran but the setup kept dumping out zero eigenvalue. Is there any approach that could help improve the simulation? thanks!
regards,
Wei
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
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
participants (3)
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ankanggao＠ustc.edu.cn
-
shan xiangjun
-
Wei He