[Nek5000-users] Problems in getting eigenvalues using ARNOLDI

nek5000-users at lists.mcs.anl.gov nek5000-users at lists.mcs.anl.gov
Tue Oct 30 00:40:19 CDT 2018


Hi Guillaume,

I tried with the help of your valuable suggestions. I am getting dominant
Eigenvalue with time period 8.34 which is very much close to the
literature. However, I require 30 Eigen values by setting P112=30 and
P111=90. Below is the eigenvalues I am getting after many restarts.

                                            re(RITZ);
im(RITZ)               ln|RITZ|;                                 arg(RITZ)
           1   0.991128702238537       0.150881402754817
1.272083634754888E-002
    0.755360071443281
           2   0.991128702238537      -0.150881402754817
1.272083634754888E-002
   -0.755360071443281
           3   0.991728721496092       1.806383192432841E-002
-4.069909517841635E-002
    9.106237555496137E-002
           4   0.991728721496092      -1.806383192432841E-002
-4.069909517841635E-002
   -9.106237555496137E-002
           5   0.989791831070271       3.446186469202143E-002
-4.827437507304033E-002
    0.174016133198715
           6   0.989791831070271      -3.446186469202143E-002
-4.827437507304033E-002
   -0.174016133198715
           7   0.987601103156919       5.049392478862426E-000
-5.585540570484418E-002
    0.255416865677410
           8   0.987601103156919      -5.049392478862426E-002
-5.585540570484418E-002
   -0.255416865677410
           9   0.995627135254111       0.000000000000000E+000
-2.191226841613384E-002
    0.000000000000000E+000
          10   0.995700191328997       0.000000000000000E+000
-2.154539716426180E-002
    0.000000000000000E+000
          11   0.995229254767405       0.000000000000000E+000
-2.391080780851450E-002
    0.000000000000000E+000
          12   0.995434205850176       0.000000000000000E+00
-2.288124611941097E-002
    0.000000000000000E+000
          13   0.994877066906734       0.000000000000000E+000
-2.568050152041379E-002
    0.000000000000000E+000
          14   0.994526533813701       0.000000000000000E+000
-2.744250243633435E-002.
   0.000000000000000E+000
          15   0.994024234181460       0.000000000000000E+000
-2.996846079257938E-002.
   0.000000000000000E+000
          16   0.992886352948494       0.000000000000000E+000
-3.569534837742794E-002
    0.000000000000000E+000
          17   0.993531725861019       0.000000000000000E+000
-3.244642035911912E-002
    0.000000000000000E+000
          18   0.992269436061858       0.000000000000000E+000
-3.880299821483946E-002
    0.000000000000000E+000
          19   0.991568951835935       0.000000000000000E+000
-4.233395244633451E-002
    0.000000000000000E+000
          20   0.991491977086931       0.000000000000000E+000
-4.272211373739676E-002
    0.000000000000000E+000
          21   0.991513431383682       0.000000000000000E+000
-4.261392292430112E-002
    0.000000000000000E+000
          22   0.991180149347166       0.000000000000000E+00
-4.429487878603097E-002
    0.000000000000000E+000
          23   0.991284115416627       0.000000000000000E+000
-4.377045031887505E-002
    0.000000000000000E+000
          24   0.990874009258556       0.000000000000000E+000
-4.583943845265666E-002
    0.000000000000000E+000
          25   0.990632850108536       0.000000000000000E+000
-4.705648774052894E-002
    0.000000000000000E+000
          26   0.990852910254318       0.000000000000000E+000
-4.594590622089855E-002.
   0.000000000000000E+000
          27   0.990206173286647       0.000000000000000E+000
-4.921050845320660E-002
    0.000000000000000E+000
          28   0.990051445648789       0.000000000000000E+000
-4.999185950921724E-002
    0.000000000000000E+000
          29   0.989332783273003       0.000000000000000E+000
-5.362259677015029E-002
    0.000000000000000E+000
          30   0.989848247701740       0.000000000000000E+000
-5.101816376314156E-002
    0.000000000000000E+000
          31   0.989278105749528       0.000000000000000E+000
-5.389893975295782E-002
    0.000000000000000E+000

   I am unable to understand the reason behind getting so many Eigenvalues
with zero imaginary part/rotation. Please help.

Regards,

On Wed, Oct 3, 2018 at 2:54 PM <nek5000-users at lists.mcs.anl.gov> wrote:

> Hi,
>
> What is your time step? I calculated the spectrum of the cylinder flow a
> while ago at Re=44 and I got an angular frequency of 0.7278, which
> corresponds to a period of 8.63.
> It is possible that 40 time steps per Arnoldi iteration is too small; a
> good start is to integrate for 1/10th of the period, so dt*p109 = 0.8
> approximately. I used 120 time steps at dt=4.2e-3 but it may be faster with
> more steps.
> It depends on which frequencies you want to resolve; if you integrate for
> a short time your operator is close to identity and all eigenvalues are
> close to 1, but if you integrate for too long then the frequencies of the
> eigenvalues you are interested in will be aliased.
>
> I think you could try decreasing p021 and p022 to maybe 1e-10 or 1e-12 and
> see if helps, too.
>
> Best,
> Guillaume
>
> On 03/10/2018 07:24, nek5000-users at lists.mcs.anl.gov wrote:
>
> Hi Guillaume,
>
> Thanks for your reply. My reply to your queries is as below:-
>
> 1) I am getting unstable pair of Eigen values with growth rate around 0.02.
> 2) Solver tolerance that I used are ;
>   7.00000              p020 NORDER
>   0.100000E-09    p021 DIVERGENCE
>   0.100000E-09.   p022 HELMHOLTZ
>    0.00000             p023 NPSCAL
>   0.100000E-09    p024 TOLREL
>   0.100000E-04    p025 TOLABS
> 1.00000E-05.       p113 : ARNOLDI: arpack tolerance
>
>
> 3) Boundary conditions are :
>
> I am using sponge strength at inlet and outlet with following details in
> .rea file
>    1.00000     p119 : SPONGE STRENGTH
>    25.0000     p120 : SPONGE TOTAL WIDTH
>    3.00000     p121 : SPONGE DROP WIDTH (INFLOW)
>    5.00000     p122 : SPONGE RISE WIDTH (OUTFLOW)
> the sponge function and its cal is detailed in userf subroutine of .usr
> file
>
> Also following is defined in .usr file
> c-----------------------------------------------------------------------
>       subroutine userbc (ix,iy,iz,iside,eg)
>
>       include 'SIZE'
>       include 'NEKUSE'          ! UX, UY, UZ, TEMP, X, Y
>       include 'PARALLEL'        ! GLLEL
>
>
>       integer e,eg
>
> c     velocity
> c      e  =  GLLEL(eg)
>       UX = 0.0
>       UY = 0.0
>       UZ = 0.0
>
> c     t
>       TEMP=0.0
>
>       return
>       end
> c-----------------------------------------------------------------------
>       subroutine useric (ix,iy,iz,ieg)
>
>       include 'SIZE'
>       include 'NEKUSE'          ! UX, UY, UZ, TEMP, Z
>
>       integer idum
>       save    idum
>       data    idum / 0 /
>
>       real eps
>
>       if (idum.eq.0) idum = 99 + nid
>       eps = 0.1
>
> c     velocity
> c     random distribution
>       UX = eps*(ran1(idum)-0.50)
>       UY = eps*(ran1(idum)-0.50)
>       UZ = eps*(ran1(idum)-0.50)
>
> c     t
>       TEMP=0
>
>       return
>       end
>
>
> 40.0000     p109 : ARNOLDI: frequency of calling arn_solve
>    4.00000     p110 : ARNOLDI: maximal number of arnoldi cycles
>   90.0000     p111 : ARNOLDI: size of Krylov space
>    30.0000     p112 : ARNOLDI: number of eigenvectors
>
>
> If I am increasing the Krylov subspace then will I get Eigen values at
> lesser restart ?
>
> Kindly help please as I am new to this. Thanks in advance.
>
> Alok Mishra
> Research Scholar
> Computational Propulsion Lab
> Aerospace Department IIT Kanpur
> +91-8795844555
>
> _______________________________________________
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>
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-- 
Alok Mishra
Research Scholar
Computational Propulsion Lab
Aerospace Department IIT Kanpur
+91-8795844555
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