Hi, I am having convergence problems with my Snapshot POD solution on channel flow with smooth wall. I have tried increasing my number of samples (snapshots), working with different sampling time intervals and overall sampling time but my first mode captures relatively low energy compared to other papers(previous studies). I have also imposed y and z reflection. For the sample size I went up to 3900 snapshots (with reflection) but my first fluctuating mode captures around 4% and I am far away from values like 30% or 50% as mentioned in the other papers. Could there be other parameters which affect convergence? I would appreciate your comments about the convergence issue.

Looking forward to hear your comments, Sincerely,

Mehmet SEN

Hi:

i am also working on the POD, would you like to give me your email address.

from your energy distribution , i think your algoritm may be some wrong

Thank you very much! ztdep@yahoo.com.cn

Hi:

I am also working on the POD, would you like to give me your email address.

from your energy distribution , i think your algoritm may be some wrong!

Thank you very much! ztdep@yahoo.com.cn

I'm not quite sure what you mean by your fluctuating mode.You should be subtracting out the mean of your data before you compute the modes. For a 2D problem if you do this, usually the first 5-10 modes will capture upwards of 99 percent of the total energy of your snapshot data.

Yes I am subtracting my mean data from all the snapshots before calculating the correlation matrix, that is why I called them fluctuating modes. I am performing a 2D SnapShotPOD on y-z plane but I am getting 90% of energy after some hundred modes out of 4000 snapshots. Is there an optimum value for domain size where we perform POD? Or any other parameters which may affect convergence? Thank you again.

Sincerely, Mehmet

How are you "exciting" the fluid as to energize the modes of interest when you are generating your snapshot data?

We are using DNS to generate the data for a smooth-channel flow for Re_t=180. A turbulent initial condition is used and the N-Sequations are solved for a long time until convergence is obtained. Beyond which data is collected for 200-400 viscous time units.

Well it might be possible that your turbulent flow has many dynamic modes which contribute. Perhaps you can check out the work of Holmes at Princeton. If I remember correctly he has done some work with POD and turbulent channel problems.