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
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*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
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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
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<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
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