Hi Spencer,

This is indeed very helpful. I have another question though.
Is it possible to enforce symmetric boundary conditions?

Consider half of a smooth channel, much like the stability test. I am trying to use the symmetric properties of the channel. I have periodic conditions at inlet and outlet, a no slip at the material wall (y=-1), and some kind of symmetric conditions at y=0 line.
You will find the mesh and an appropriate session file in the attachment.

Best regards!
Stan Gepner

On 31.10.2015 05:21, Sherwin, Spencer J wrote:
Hi Stan,

I believe the issue may be due to the modified Arnoldi algorithm which seems fine for getting a leading eigenvalue but not to get a sub-spectrum.  Using Arpack which has to be compiled from a third party package (On Mac we typically use macports to install it) would be an option. Generally Arpack does not give you such a clear convergence history when it is iterating but it does some post-processing to clean up the eigenvalues and get a better sub-spectrum. This improvement i believe is due to using the A-norm when running the Arnoldi algorithm.

We recently ran a tutorial on using this which I attach and we hope to get on the web page soon. The associated files are downloadable from the web.

In this tutorial you will also see there is a coupled linearised Navier Stokes solver where you can add a shift so this is probably the approach where you can get to more of the spectrum of your problem. Note that using this solver you need a much larger kdim spectrum.

Finally the .fld file that is dumped is a mix of the eigenvalues. It essentially contains the sub-spectrum that the Arnoldi method is iterating on at the time the iterations complete.

Hope this answers your question.

Cheers,
Spencer.





On 31 Oct 2015, at 01:11, Stanisław Gepner <sgepner@meil.pw.edu.pl> wrote:

> Dear All,
>
> I am encountering some trouble when performing stability analysis of a channel flow. I am trying to track an instability as I modify flow conditions and channel geometry.
>
> I managed to reproduce the problem I am having with my calculations with the ChannelStability test. I start by running the unmodified ChannelStability.xml, looking for 2 modes, using kdim=16 at Re=7500. In a matter of a couple iterations I get the expected solution:
>
>        Magnitude            Angle         Growth Frequency      Residual
> EV:  0  1.0003e+00  3.4978e-02  2.2341e-03  2.4984e-01  9.3618e-07
> EV:  1  1.0003e+00 -3.4978e-02  2.2341e-03 -2.4984e-01  9.3618e-07
> EV:  2  9.7225e-01  2.0326e+00 -2.0099e-01  1.4519e+01  2.7629e-01
> EV:  3  9.7225e-01 -2.0326e+00 -2.0099e-01 -1.4519e+01  2.7629e-01
> ...
>
> Now I want to get 4 modes. I know there are going to be modes with negative growth. As I run the calculations at some point there appears an eigenvalue with zero imaginary part (zero angle, frequency) and slowly grows, to the point that it becomes dominant, and produces some trashy result. As in the example below.
>
>        Magnitude   Angle       Growth      Frequency   Residual
> EV:  0  1.0004e+00  4.9969e-02  2.2362e-03  2.4984e-01  7.9474e-08
> EV:  1  1.0004e+00 -4.9969e-02  2.2362e-03 -2.4984e-01  7.9474e-08
> EV:  2  1.0513e+00  0.0000e+00  2.5017e-01  0.0000e+00  2.2509e-06
> EV:  3  9.8487e-01  2.3743e+00 -7.6211e-02  1.1871e+01  2.4000e-02
> EV:  4  9.8487e-01 -2.3743e+00 -7.6211e-02 -1.1871e+01  2.4000e-02
> ...
>
> I tried increasing the size of the vector space, but with the same result. Than I tried to decrease the time scale. This has an effect of impacting the convergence, and finally also produces zero frequency mode. Should I understand this is a bad idea to use time stepping approach to look for decaying modes?
> To test this I tried running the ChannelStability test lowering the Reynolds number to 2000 and recovering results available in literature [1]. I think, that since I used the ChannelStability.rst as a starting point the recovered values are close to those for the Orr-Sommerfeld (growth=-0.01979866, w=0.3121003). Still, at Re=2000 it is the Squire mode that is decaying slower (s=-0.016), but I suspect that due to my starting point I will not reach it.
>
> I also have a general question regarding the stability. What is the content of the .fld file produced at the end of stability calculations? Is it a linear combinations of the vectors currently locked in the vector space?
> Also, is there a way to have a "broader look" at the eigen spectrum?
>
> Cheers,
> Stan Gepner
>
> [1] Stability and Transition in Shear Flows. By P. J. Schmid & D. S. Henningson. p. 506, Springer, 2001
>
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Spencer  Sherwin
McLaren Racing/Royal Academy of Engineering Research Chair,
Professor of Computational Fluid Mechanics,
Department of Aeronautics,
Imperial College London
South Kensington Campus
London SW7 2AZ

s.sherwin@imperial.ac.uk
+44 (0) 20 759 45052