Stability of channel flow with Nektar++
Dear Sirs, First of all thank you for developing this great software and making it available. I am planing to investigate stability of an incompressible channel flow using Nektar. I have studied the manual and the source (the version from the git repo) and repeated some of the examples from the IncNavierStokesSolver folders Tests and Examples. The channel flow stability test (Tests/ChanStability.xml) uses a base flow (.bse) and an initial guess (.rst) and converges to an expected result. Now, as practice I tried to play around with the settings, first by changing the Driver to Arpack (this works as well). Since I might not know the initial approximation I tried to get rid of the initial guess, and replaceed it with some random initial vector (I have put zeros, non zeros, the awgn()). This time the problem did not coverage at all (I increased the numbers of iterations, tried to modify the number and size of the time steps, change the dimension of the Krylov space). Is this an expected behaviour? And since this is a test, the problem is set up to be small and quick and would only converge with the proper initial vector? Should I expect a similar problem for a larger 3D case? My second question concerns the base flow. I tried to recover the base flow using the stationary solver (both classical and adaptive) but I failed. Could you point me at an example of how to set this up? Also I noticed (or I think I did) that the Example/ChanStability-Base.xml does not produce a correct flow field. Am I right? I would appreciate if you would comment on my questions. Best Regards, Stan Gepner
Hi Stan, Thanks for your feedback. The channel flow stability test (Tests/ChanStability.xml) uses a base flow (.bse) and an initial guess (.rst) and converges to an expected result. Now, as practice I tried to play around with the settings, first by changing the Driver to Arpack (this works as well). Since I might not know the initial approximation I tried to get rid of the initial guess, and replaceed it with some random initial vector (I have put zeros, non zeros, the awgn()). This time the problem did not coverage at all (I increased the numbers of iterations, tried to modify the number and size of the time steps, change the dimension of the Krylov space). Is this an expected behaviour? And since this is a test, the problem is set up to be small and quick and would only converge with the proper initial vector? Should I expect a similar problem for a larger 3D case? It should converge. Quite possibly having zero initial conditions might cause problems but having non-zero or awgn() should have worked. It can take quite a few iterations since the channel problem has a very small growth rate. As you note we have a simplified regression test to make sure it does not take too long to run. Can I ask if you were using the 2.5D instability ( a Fourier mode in the span wise direction) or the 2D instability. We did have an issue with the 2.5D code which has recently been fixed and I think is part of the current Master on the repository (Chris can you confirm if this is true). Can I first check you are using the most recent version of Master? My second question concerns the base flow. I tried to recover the base flow using the stationary solver (both classical and adaptive) but I failed. Could you point me at an example of how to set this up? Also I noticed (or I think I did) that the Example/ChanStability-Base.xml does not produce a correct flow field. Am I right? Again can we find out which stationary solver you were running. Was this using the Selective frequency damping? If so perhaps Bastien can help check what might be going on here. Alternatively we tend to run base flows using the time marching methods until they get to a steady state. I have just run the ChanStability-Base.xml case and get an error of L 2 error (variable u) : 0.00187368 L inf error (variable u) : 0.000533519 L 2 error (variable v) : 1.21301e-11 L inf error (variable v) : 6.97233e-10 L 2 error (variable p) : 6.41086e-10 L inf error (variable p) : 2.31381e-10 which does not seem correct. Is this also the answer you observe (note I only ran it for 2000 steps). Cheers, Spencer. I would appreciate if you would comment on my questions. Best Regards, Stan Gepner _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users 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<mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052
Hi,
Can I ask if you were using the 2.5D instability ( a Fourier mode in the span wise direction) or the 2D instability. We did have an issue with the 2.5D code which has recently been fixed and I think is part of the current Master on the repository (*Chris* can you confirm if this is true). Can I first check you are using the most recent version of Master?
I think I used the 2D case. The config is the one found in Tests/ChanStability.xml (it is 2D right?). I actually left it ruining for 2 days on a cluster but it did not converge (with non zero initial vector) I pulled from git just yesterday.
Again can we find out which stationary solver you were running. Was this using the Selective frequency damping? If so perhaps Bastien can help check what might be going on here. Alternatively we tend to run base flows using the time marching methods until they get to a steady state. I was trying to use the SFD solver (both adaptive and classical). Are there any other stationary solvers? I have found an example in Tests/Cyl_AdaptiveSFD of how to set this up. Again if run with the initial flow, and eigenvector this works like a charm. But if I run it from scratch I have problems with convergence. (All I do is replace the InitialConditions).
Also I noticed (or I think I did) that the Example/ChanStability-Base.xml does not produce a correct flow field. Am I right?
I have just run the ChanStability-Base.xml case and get an error of
L 2 error (variable u) : 0.00187368 L inf error (variable u) : 0.000533519 L 2 error (variable v) : 1.21301e-11 L inf error (variable v) : 6.97233e-10 L 2 error (variable p) : 6.41086e-10 L inf error (variable p) : 2.31381e-10
which does not seem correct. Is this also the answer you observe (note I only ran it for 2000 steps).
I am getting similar result. If I visualize it with ParaView it does not look as expected. I thing there is a problem with the Forcing, and the use or Periodic BCs. Is it not a problem to applay periodic conditions on pressure, without specifying a body force (pressure gradient)? Regarding the Periodic BCs, are you aware if it is possible to apply a fixed mass flux (I looked through the code and I think it is not, but if it is, please correct me). Best regards, Stanisław Gepner
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
_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
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
_______________________________________________ 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
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
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
_______________________________________________ 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
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
Hi Stan, I believe it should be possible since I have used these conditions in the past where the normal velocity is set to Dirichlet zero and other components have Zero Neumann conditions. Is this what you mean? Looking at your file it would seem so. Sorry have not had a chance to run your case yet. Is it executing? I believe I have used this with the 2.5D but do not know if it has been tested in purely 2d. Cheers, Spencer On 2 Nov 2015, at 22:52, Stanisław Gepner <sgepner@meil.pw.edu.pl<mailto:sgepner@meil.pw.edu.pl>> wrote: 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 <mailto:sgepner@meil.pw.edu.pl> <sgepner@meil.pw.edu.pl><mailto: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
_______________________________________________ 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
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<mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052 <s0.00.zip>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users 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<mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052
Hi Spencer, On 04.11.2015 14:09, Sherwin, Spencer J wrote:
Hi Stan,
I believe it should be possible since I have used these conditions in the past where the normal velocity is set to Dirichlet zero and other components have Zero Neumann conditions. Is this what you mean? Looking at your file it would seem so. This is exactly what I was intending. I was expecting that, accordingly to the mix of Neuman / Dirichlet conditions, I would get symmetric / anti symmetric spectrum. However when run, I am getting results that do not correspond to any found for the full channel case. Also the modes, when looked at in Paraview seem wrong.
Sorry have not had a chance to run your case yet. Is it executing? I believe I have used this with the 2.5D but do not know if it has been tested in purely 2d. It is executing. Might be there is something wrong with my geometry. It is rather simple, but still, I could have overlooked something. I tested it running the non stationary solver, and the results seemed as expected for a symmetric channel.
I will try to run a 2.5D case using this geometry and report what I find. Best Regards, Stan Gepner
Cheers, Spencer
On 2 Nov 2015, at 22:52, Stanisław Gepner <sgepner@meil.pw.edu.pl <mailto:sgepner@meil.pw.edu.pl>> wrote:
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
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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 <mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052
Hi Spencer, I run the 2D symmetry case, modifying the type of boundary conditions. I managed to reproduce a growth rate of the ChanStability case from the tests (Re=7500). What confused me is that, with the symmetry, the dominant mode is not the first one anymore. In fact I recovered it as 24/25. I was recovering only 16 before. On the other hand, I got less error when compared with the Orr-Sommerfeld solution. So the 2D symmetry works. Best regards, Stan Gepner On 04.11.2015 14:50, Stanisław Gepner wrote:
Hi Spencer,
On 04.11.2015 14:09, Sherwin, Spencer J wrote:
Hi Stan,
I believe it should be possible since I have used these conditions in the past where the normal velocity is set to Dirichlet zero and other components have Zero Neumann conditions. Is this what you mean? Looking at your file it would seem so. This is exactly what I was intending. I was expecting that, accordingly to the mix of Neuman / Dirichlet conditions, I would get symmetric / anti symmetric spectrum. However when run, I am getting results that do not correspond to any found for the full channel case. Also the modes, when looked at in Paraview seem wrong.
Sorry have not had a chance to run your case yet. Is it executing? I believe I have used this with the 2.5D but do not know if it has been tested in purely 2d. It is executing. Might be there is something wrong with my geometry. It is rather simple, but still, I could have overlooked something. I tested it running the non stationary solver, and the results seemed as expected for a symmetric channel.
I will try to run a 2.5D case using this geometry and report what I find.
Best Regards, Stan Gepner
Cheers, Spencer
On 2 Nov 2015, at 22:52, Stanisław Gepner <sgepner@meil.pw.edu.pl> wrote:
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
_______________________________________________ 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
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
<s0.00.zip>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk <mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users
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 <mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052
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participants (2)
-
Sherwin, Spencer J
-
Stanisław Gepner