[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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