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<mailto:abhishek.kir@gmail.com> 发送时间: 2021年11月1日 19:37 收件人: Daiane Iglesia Dolci<mailto:daia.dolci@gmail.com> 抄送: shan xiangjun<mailto:x_j_shan@outlook.com>; nektar-users@imperial.ac.uk<mailto: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<mailto: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<mailto: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<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 -- _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users -- Daiane Iglesia Dolci (dolci@usp.br/daia.dolci@gmail.com<http://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<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users