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*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 版邮件发送

 

发件人: Sherwin, Spencer J
发送时间: 2021年11月1日 1:55
收件人: Abhishek Kumar
抄送: shan xiangjun; nektar-users
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

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

 

<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 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


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