Hi Xiangjun, According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. I have reproduced Giannetti and Luchini's result for Re = 50 (attached in this email) using Nektar++. To do this multiplication, I first rename the variables of direct and adjoints modes obtained from the stability analysis. Then put them into a single file using FieldConvert. Now, rest calculations can be done inside ParaView or Visit. With regards --------------------------------------------------------------------------------------- Abhishek Kumar Assistant Professor (Research) Centre for Fluid and Complex Systems Coventry University, Coventry CV15FB The United Kingdom Web: https://sites.google.com/view/abhishekkir --------------------------------------------------------------------------------------- [image: visit0006.png] On Wed, Oct 27, 2021 at 10:17 PM Sherwin, Spencer J < s.sherwin@imperial.ac.uk> wrote:

Dear Xiangjun,

I believe the sensitivity plots are related to the inner product of the adjoint and forward modes. I am afraid I do not recall which inner products gives you which sensitivities.

Cheers, Spencer.

On 27 Oct 2021, at 08:31, shan xiangjun <x_j_shan@outlook.com> wrote:

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 all:

I want to use the Nektar++ to conduct structural sensitivity analysis on the flow problem. I can get direct and adjoint modes, but I don't know how to get the sensitivity of base flow modification and local feedback (as shown in figure).

Can anyone help me?

Looking forward to your reply!

Best regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

<2021-10-23_8-46-11.jpg>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

--

Dear Spenser and Kumar ： I still haven't got the correct sensitivity map. Now I'm a little confused and don't know whether my understanding is correct. According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. So, I think I should calculate this outer product and get a tensor. But it doesn't seem easy to get. Using the concatenate module of Fieldconvert, I put the two eig.fld files obtained from stability analysis into a single conc.fld file and convert it into the .vtu format. It contains four variables u1, v1, u2 and v2. And then I imported it into ParaView to compute the dyadic product. I tried the Calculator filter first, constructed vector a=u1*iHat+v1*jHat and vector b =u2*iHat+v2*jHat, and intend to do the dyadic product with these two vectors. But I can't find the function of dyadic product in the Calculator filter. Similarly, Python Calculator can also get vectors a and b, but the numpy.outer() cannot be calculated. I also tried Programmable Filter and didn't succeed either. This does not seem to work on the .vtu format. I am not very proficient in Paraview and Python. Could I ask you about the specific process of getting the sensitivity plots? Best regards, Xiangjun Shan 从 Windows 版邮件<https://go.microsoft.com/fwlink/?LinkId=550986>发送 发件人: Sherwin, Spencer J<mailto:s.sherwin@imperial.ac.uk> 发送时间: 2021年11月1日 1:55 收件人: Abhishek Kumar<mailto:abhishek.kir@gmail.com> 抄送: shan xiangjun<mailto:x_j_shan@outlook.com>; nektar-users<mailto:nektar-users@imperial.ac.uk> 主题: Re: [Nektar-users] How to do sensitivity analysis? HI Both, Yep I agree this is a good way to do it. Cheers, Spencer. On 29 Oct 2021, at 22:07, Abhishek Kumar <abhishek.kir@gmail.com<mailto:abhishek.kir@gmail.com>> wrote: Hi Xiangjun, According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. I have reproduced Giannetti and Luchini's result for Re = 50 (attached in this email) using Nektar++. To do this multiplication, I first rename the variables of direct and adjoints modes obtained from the stability analysis. Then put them into a single file using FieldConvert. Now, rest calculations can be done inside ParaView or Visit. With regards --------------------------------------------------------------------------------------- Abhishek Kumar Assistant Professor (Research) Centre for Fluid and Complex Systems Coventry University, Coventry CV15FB The United Kingdom Web: https://sites.google.com/view/abhishekkir --------------------------------------------------------------------------------------- <visit0006.png> On Wed, Oct 27, 2021 at 10:17 PM Sherwin, Spencer J <s.sherwin@imperial.ac.uk<mailto:s.sherwin@imperial.ac.uk>> wrote: Dear Xiangjun, I believe the sensitivity plots are related to the inner product of the adjoint and forward modes. I am afraid I do not recall which inner products gives you which sensitivities. Cheers, Spencer. On 27 Oct 2021, at 08:31, shan xiangjun <x_j_shan@outlook.com<mailto:x_j_shan@outlook.com>> wrote: This email from x_j_shan@outlook.com<mailto: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 all: I want to use the Nektar++ to conduct structural sensitivity analysis on the flow problem. I can get direct and adjoint modes, but I don't know how to get the sensitivity of base flow modification and local feedback (as shown in figure). Can anyone help me? Looking forward to your reply! Best regards, Xiangjun Shan 从 Windows 版邮件<https://go.microsoft.com/fwlink/?LinkId=550986>发送 <2021-10-23_8-46-11.jpg>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users --

Hi Shan, It is good to normalise, but still it will work with Nektar++'s normalisation (only colorbar will be different from Giannetti and Luchini JFM 2007). Now to plot ||*u*| ||*u_adj*|| you need both the real and imaginary part of the direct and adjoint modes. To obtain real and imaginary part you should put nvec=2 in the session file, and take eig_0 as real and eig_1 as imag. In paraview, you can do following: ||*u*|| ||*u_adj*|| = sqrt((u_real^2)+(v_real^2)+(u_imag^2)+(v_imag^2) + (u_adj_real^2)+(v_adj_real^2)+(u_adj_imag^2)+(v_adj_imag^2)). Here *u* is the direct mode and *u_adj* is the adjoint mode. With regards Abhishek On Mon, Nov 1, 2021 at 10:58 AM Daiane Iglesia Dolci <daia.dolci@gmail.com> wrote:

Hi Xiangjun,

It is necessary to normalize the adjoint mode to reach the integral of u_adj*u_direct+v_adj*v_direct equal to 1 (see Fig. attached, it is a print of eq. 2.8 from Giannetti and Luchini JFM 2007). Next, you can compute the sensitivity with u_adj normalized. This way, you will find a match with Giannetti and Luchini JFM 2007 results.

Regards,

Dolci.

Em seg., 1 de nov. de 2021 às 04:27, shan xiangjun <x_j_shan@outlook.com> escreveu:

...

Dear Spenser and Kumar ：

I still haven't got the correct sensitivity map. Now I'm a little confused and don't know whether my understanding is correct. According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. So, I think I should calculate this outer product and get a tensor. But it doesn't seem easy to get.

Using the * concatenate *module of *Fieldconvert*, I put the two eig.fld files obtained from stability analysis into a single conc.fld file and convert it into the *.vtu* format. It contains four variables u1, v1, u2 and v2. And then I imported it into ParaView to compute the dyadic product.

I tried the *Calculator filter *first, constructed vector *a*=u1**iHa* t+v1**jHat* and vector b =u2**iHat*+v2**jHat*, and intend to do the dyadic product with these two vectors. But I can't find the function of dyadic product in the *Calculator filter.*

Similarly, *Python Calculator *can also get vectors a and b, but the *numpy.outer()* cannot be calculated.

I also tried *Programmable Filter *and didn't succeed either. This does not seem to work on the .*vtu* format.

I am not very proficient in Paraview and Python. Could I ask you about the specific process of getting the sensitivity plots?

Best regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

*发件人: *Sherwin, Spencer J <s.sherwin@imperial.ac.uk> *发送时间: *2021年11月1日 1:55 *收件人: *Abhishek Kumar <abhishek.kir@gmail.com> *抄送: *shan xiangjun <x_j_shan@outlook.com>; nektar-users <nektar-users@imperial.ac.uk> *主题: *Re: [Nektar-users] How to do sensitivity analysis?

HI Both,

Yep I agree this is a good way to do it.

Cheers,

Spencer.

On 29 Oct 2021, at 22:07, Abhishek Kumar <abhishek.kir@gmail.com> wrote:

Hi Xiangjun,

According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. I have reproduced Giannetti and Luchini's result for Re = 50 (attached in this email) using Nektar++.

To do this multiplication, I first rename the variables of direct and adjoints modes obtained from the stability analysis. Then put them into a single file using FieldConvert. Now, rest calculations can be done inside ParaView or Visit.

With regards

---------------------------------------------------------------------------------------

Abhishek Kumar

Assistant Professor (Research)

Centre for Fluid and Complex Systems

Coventry University, Coventry CV15FB

The United Kingdom

Web: https://sites.google.com/view/abhishekkir

---------------------------------------------------------------------------------------

<visit0006.png>

On Wed, Oct 27, 2021 at 10:17 PM Sherwin, Spencer J < s.sherwin@imperial.ac.uk> wrote:

Dear Xiangjun,

I believe the sensitivity plots are related to the inner product of the adjoint and forward modes. I am afraid I do not recall which inner products gives you which sensitivities.

Cheers,

Spencer.

On 27 Oct 2021, at 08:31, shan xiangjun <x_j_shan@outlook.com> wrote:

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 all:

I want to use the Nektar++ to conduct structural sensitivity analysis on the flow problem. I can get direct and adjoint modes, but I don't know how to get the sensitivity of base flow modification and local feedback (as shown in figure).

Can anyone help me?

Looking forward to your reply!

Best regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

<2021-10-23_8-46-11.jpg>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

--

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

-- Daiane Iglesia Dolci (dolci@usp.br/daia.dolci@gmail.com) Post-Doctoral Researcher at Research Centre for Gas Innovation (RCGI) and Fluid & Dynamics Research Group (NDF) Escola Politécnica, Universidade de São Paulo Schedule a meeting here <https://calendly.com/ig-dolci>

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

Hi Xiangjun, Excellent. I will talk more about receptivity and sensitivity for mixed baroclinic convection in the upcoming Nektar++ workshop. With regards Abhishek On Tue, Nov 2, 2021 at 8:08 AM shan xiangjun <x_j_shan@outlook.com> wrote:

Hi Abhishek:

That’s so kind of you!

I have got the sensitivity map following your steps.

Thank you so much for everyone’s help, I have benefited a lot.

Best Regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

*发件人: *Abhishek Kumar <abhishek.kir@gmail.com> *发送时间: *2021年11月1日 19:37 *收件人: *Daiane Iglesia Dolci <daia.dolci@gmail.com> *抄送: *shan xiangjun <x_j_shan@outlook.com>; nektar-users@imperial.ac.uk <Nektar-users@imperial.ac.uk> *主题: *Re: [Nektar-users] 回复: How to do sensitivity analysis?

Hi Shan,

It is good to normalise, but still it will work with Nektar++'s normalisation (only colorbar will be different from Giannetti and Luchini JFM 2007). Now to plot ||*u*| ||*u_adj*|| you need both the real and imaginary part of the direct and adjoint modes. To obtain real and imaginary part you should put nvec=2 in the session file, and take eig_0 as real and eig_1 as imag. In paraview, you can do following:

||*u*|| ||*u_adj*|| = sqrt((u_real^2)+(v_real^2)+(u_imag^2)+(v_imag^2) + (u_adj_real^2)+(v_adj_real^2)+(u_adj_imag^2)+(v_adj_imag^2)).

Here *u* is the direct mode and *u_adj* is the adjoint mode.

With regards

Abhishek

On Mon, Nov 1, 2021 at 10:58 AM Daiane Iglesia Dolci <daia.dolci@gmail.com> wrote:

Hi Xiangjun,

It is necessary to normalize the adjoint mode to reach the integral of u_adj*u_direct+v_adj*v_direct equal to 1 (see Fig. attached, it is a print of eq. 2.8 from Giannetti and Luchini JFM 2007). Next, you can compute the sensitivity with u_adj normalized. This way, you will find a match with Giannetti and Luchini JFM 2007 results.

Regards,

Dolci.

Em seg., 1 de nov. de 2021 às 04:27, shan xiangjun <x_j_shan@outlook.com> escreveu:

Dear Spenser and Kumar ：

I still haven't got the correct sensitivity map. Now I'm a little confused and don't know whether my understanding is correct. According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. So, I think I should calculate this outer product and get a tensor. But it doesn't seem easy to get.

Using the *concatenate *module of *Fieldconvert*, I put the two eig.fld files obtained from stability analysis into a single conc.fld file and convert it into the *.vtu* format. It contains four variables u1, v1, u2 and v2. And then I imported it into ParaView to compute the dyadic product.

I tried the *Calculator filter *first, constructed vector *a*=u1**iHa* t+v1**jHat* and vector b =u2**iHat*+v2**jHat*, and intend to do the dyadic product with these two vectors. But I can't find the function of dyadic product in the *Calculator filter.*

Similarly, *Python Calculator *can also get vectors a and b, but the *numpy.outer()* cannot be calculated.

I also tried *Programmable Filter *and didn't succeed either. This does not seem to work on the .*vtu* format.

I am not very proficient in Paraview and Python. Could I ask you about the specific process of getting the sensitivity plots?

Best regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

*发件人: *Sherwin, Spencer J <s.sherwin@imperial.ac.uk> *发送时间: *2021年11月1日 1:55 *收件人: *Abhishek Kumar <abhishek.kir@gmail.com> *抄送: *shan xiangjun <x_j_shan@outlook.com>; nektar-users <nektar-users@imperial.ac.uk> *主题: *Re: [Nektar-users] How to do sensitivity analysis?

HI Both,

Yep I agree this is a good way to do it.

Cheers,

Spencer.

On 29 Oct 2021, at 22:07, Abhishek Kumar <abhishek.kir@gmail.com> wrote:

Hi Xiangjun,

According to Giannetti and Luchini JFM 2007, sensitivity is the dyadic product of direct and adjoint modes. I have reproduced Giannetti and Luchini's result for Re = 50 (attached in this email) using Nektar++.

To do this multiplication, I first rename the variables of direct and adjoints modes obtained from the stability analysis. Then put them into a single file using FieldConvert. Now, rest calculations can be done inside ParaView or Visit.

With regards

---------------------------------------------------------------------------------------

Abhishek Kumar

Assistant Professor (Research)

Centre for Fluid and Complex Systems

Coventry University, Coventry CV15FB

The United Kingdom

Web: https://sites.google.com/view/abhishekkir

---------------------------------------------------------------------------------------

<visit0006.png>

On Wed, Oct 27, 2021 at 10:17 PM Sherwin, Spencer J < s.sherwin@imperial.ac.uk> wrote:

Dear Xiangjun,

I believe the sensitivity plots are related to the inner product of the adjoint and forward modes. I am afraid I do not recall which inner products gives you which sensitivities.

Cheers,

Spencer.

On 27 Oct 2021, at 08:31, shan xiangjun <x_j_shan@outlook.com> wrote:

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 all:

I want to use the Nektar++ to conduct structural sensitivity analysis on the flow problem. I can get direct and adjoint modes, but I don't know how to get the sensitivity of base flow modification and local feedback (as shown in figure).

Can anyone help me?

Looking forward to your reply!

Best regards,

Xiangjun Shan

从 Windows 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>发送

<2021-10-23_8-46-11.jpg>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

--

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

--

Daiane Iglesia Dolci (dolci@usp.br/daia.dolci@gmail.com)

Post-Doctoral Researcher at Research Centre for Gas Innovation (RCGI) and Fluid & Dynamics Research Group (NDF)

Escola Politécnica, Universidade de São Paulo

Schedule a meeting here <https://calendly.com/ig-dolci>

_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

--