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Hi Neks,<br>
<br>
I tried to simulated steady flow by setting the logical operator
IFTRAN = F but the simulation still runs in transient mode, How do I
get a steady time independent solution so that I can use it as my
Initial Condition ? <br>
<br>
Thank you, <br>
Kamal<br>
<br>
<br>
<div class="moz-cite-prefix">On 29/01/2014 16:01,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:<br>
</div>
<blockquote
cite="mid:mailman.12352.1391007940.3278.nek5000-users@lists.mcs.anl.gov"
type="cite">Hello Paul,
<br>
<br>
Thanks for the vorticity output and it worked.
<br>
<br>
<br>
1) I created a set-obj() for my pipe but how can I be sure that it
has taken the full pipe wall surface in to account ?
<br>
I have attached the divpipe.usr file for your reference could
you please take a look at it.
<br>
<br>
2) I even took torque_calc in to the .usr file and it gives out
something like this
<br>
<br>
200 1.00000000000E+00 -9.76942759878E-06 -8.98721249598E-06
-7.82215102801E-07 1torqx
<br>
200 1.00000000000E+00 -6.69169235606E-06 -6.35251009840E-06
-3.39182257669E-07 1torqy
<br>
200 1.00000000000E+00 9.50518561890E-10 1.50349344990E-13
9.50368212545E-10 1torqz
<br>
<br>
if I am not wrong are these the value of surface integral of
viscous force in three components of velocity along three
directions taken in the set_obj() ?
<br>
<br>
because I would like to calculate this
<br>
<br>
C_v = F^v / ( d^2 * rho * U^2 ) = double integral ( 1/Re * (du
/ dr) ) dtheta dz
<br>
<br>
<br>
Thank you,
<br>
<br>
Kamal.
<br>
<br>
<br>
On 24/01/2014 13:02, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<blockquote type="cite">
<br>
<br>
<br>
Kamal,
<br>
<br>
1) yes
<br>
<br>
2) standard approach to seeing vorticity would be something
<br>
like the following in userchk
<br>
<br>
parameter (lt=lx1*ly1*lz1*lelt)
<br>
common /myjunk/ vort(lt,3),w1(lt),w2(lt)
<br>
logical ifxyt
<br>
integer ivout ! flag to turn geometry on/off for VisIt
<br>
save ivout
<br>
data ivout /0/
<br>
<br>
<br>
if (mod(istep,iostep).eq.0) then
<br>
call comp_vort3(vort,w1,w2,vx,vy,vz)
<br>
<br>
ifxyt = ifxyo ! put geometry into first vrt file
<br>
ifxyo = .false.
<br>
if (ivout.eq.0) ifxyo = .true.
<br>
ivout = 1
<br>
<br>
call outpost(vort(1,1),vort(1,2),vort(1,3),pr,t,'vrt')
<br>
<br>
ifxyo = ifxyt ! restore ifxyo flag to original state
<br>
<br>
endif
<br>
<br>
<br>
If your session name is blah, this piece of code will put
<br>
vorticity into a sequence of files vrtblah0.f0000n
<br>
<br>
You can instead ignore the vrt prefix and the part about the
<br>
geometry with a simpler code
<br>
<br>
parameter (lt=lx1*ly1*lz1*lelt)
<br>
common /myjunk/ vort(lt,3),w1(lt),w2(lt)
<br>
<br>
if (mod(istep,iostep).eq.0) then
<br>
call comp_vort3(vort,w1,w2,vx,vy,vz)
<br>
call outpost(vort(1,1),vort(1,2),vort(1,3),pr,t,'vrt')
<br>
endif
<br>
<br>
I usually go for this latter approach, but the choice is
<br>
totally up to you.
<br>
<br>
Paul
<br>
<br>
<br>
<br>
<br>
<br>
On Fri, 24 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hello Paul,
<br>
<br>
Thanks for your reply. I am looking into the .usr file for
defining the set_obj ().
<br>
<br>
1) Could you please tell me what is 'Enter the number of
levels ?' in n2to3
<br>
<br>
is it the number of elements in Z direction ?
<br>
<br>
2) As you said about storing the computed vorticity in
velocity field to view in VisIT, I found the routine to
compute the vorticity but I am stuck about adding it to the
velocity filed to VisIT ? could you please tell me how it
works or any example which stores vorticity to the .fld file
as a separate variable.
<br>
<br>
<br>
Thank you
<br>
<br>
Kamal
<br>
<br>
<br>
On 22/01/2014 16:53, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<blockquote type="cite">Axial viscous stress is given by
torq_calc -- that's no problem whatsoever. You get a number
as a
<br>
function of time.
<br>
<br>
You can even get stresses on multiple subsets of the
geometry (e.g., if you had multiple branches
<br>
in the domain or multiple cylinders. The drag, which is a
byproduct of the torque computation (which
<br>
you can ignore), is given in terms of the viscous and
pressure components separately and as the
<br>
sum of the two.
<br>
<br>
You can identify domain boundaries by checking the boundary
conditions. Here, I recommend
<br>
looking at the set_obj routines in several of the /example
cases.
<br>
<br>
<br>
________________________________________
<br>
From: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>] on behalf of
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>]
<br>
Sent: Wednesday, January 22, 2014 9:37 AM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe with expansion
<br>
<br>
Hello Paul
<br>
<br>
I was thinking about taking the tangential velocity near to
the wall so that I can figure out my length of the
recirculation region.
<br>
<br>
Is it possible for me to access the boundary elements of the
mesh ??? so that I can take the boundary element and then
obtain the velocity at that point so that I can figure out
the length of my recirculation region.
<br>
<br>
or take the *.fld file and read it to plot the datas I need.
<br>
<br>
<br>
I also want to calculate the axial viscous force acting on
the entire pipe.
<br>
<br>
which is given by
<br>
<br>
C_v = F^v / ( d^2 * rho * U^2 ) = double integral ( 1/Re
* (du / dr) ) dtheta dz
<br>
<br>
<br>
On Jan 22, 2014, at 4:07 PM, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
As I thought about it some more, if you're interested in
the local wall shear stress
<br>
magnitude I'm quite certain you can get this by plotting
the magnitude of vorticity
<br>
on the surface in question. (Note that the sign of the
WSS, which in fact is a tensor
<br>
or a vector when restricted to a given surface, is lost in
this process, but that might
<br>
not be relevant for your needs.) If that works, then you
can readily compute the
<br>
vorticity using one of the routines in nek and store the
result in a velocity field, then
<br>
view that field with VisIt. Of course WSS will require
multiplication by viscosity.
<br>
<br>
hth,
<br>
<br>
Paul
<br>
<br>
________________________________________
<br>
From: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>] on behalf of
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>]
<br>
Sent: Tuesday, January 21, 2014 10:33 AM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe with expansion
<br>
<br>
Hi paul,
<br>
<br>
can I make this to be drag or shear quantities to be
return to the a
<br>
separate file so that it will easy for me to plot.
<br>
<br>
By the way it gives the integral quantity. Think for
example I need to
<br>
find the shear stress on the wall from the inlet to
outlet at a
<br>
particular time = 2 . How can I do that ?
<br>
<br>
Is there way to find the number of elements in x,y and z
direction ?
<br>
<br>
On 21/01/2014 17:32, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
Your integrated drag quantities should be written to the
logfile
<br>
(stdout),
<br>
assuming you've set the arguments in the call to be
.true.
<br>
<br>
Paul
<br>
<br>
On Tue, 21 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I checked the set_obj subroutine and implemented one
in my .USR file.
<br>
The code seem to run without any errors but I don't
find where these
<br>
variables are getting stored.
<br>
<br>
I use VisIT to visualize my output, even there was no
change in it.
<br>
<br>
do I have to define my own output file and write the
variables out ?
<br>
<br>
Thanks,
<br>
<br>
Kamal.
<br>
<br>
<br>
On 20/01/2014 21:52, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
You'll need to compute your own tke by manipulating
the
<br>
velocity fields.
<br>
<br>
You can get running averages of the requisite
quantities
<br>
via calls to "avg_all" which is found in navier5.f
<br>
<br>
You can compute shear stress on the wall simply by
computing
<br>
the drag on the wall, which can be done via a call
to torque_calc(),
<br>
also found in navier5.f
<br>
<br>
If you cd to /examples and type:
<br>
<br>
grep torq */*.usr
<br>
<br>
you'll find many examples of calls to torque_calc.
You simply
<br>
need to prescribe the surfaces on which shear is to
be integrated.
<br>
<br>
I typically write a routine "set_obj" to identify
such surfaces
<br>
on the first call to usrchk.
<br>
<br>
grep set_obj */*.usr
<br>
<br>
will show similar examples.
<br>
<br>
I would recommend trying this for laminar Poiseiulle
flow in
<br>
a very simple channel just to check that your calls
are properly
<br>
set.
<br>
<br>
Best,
<br>
<br>
Paul
<br>
<br>
<br>
On Mon, 20 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
Thanks and that helped.
<br>
<br>
Where can I find the variables like Turbulent KE ,
shear stress on
<br>
the wall. ?
<br>
<br>
Do i have to activate some parameters for
calculating them ?
<br>
<br>
If I had to plot them.
<br>
<br>
Thanks,
<br>
Kamal
<br>
<br>
<br>
On Jan 20, 2014, at 5:41 AM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
Looks good.
<br>
<br>
I'm guessing that one further refinement would
be:
<br>
<br>
if (z.gt.z0) scale = 1 + (smax-1)*(z-z0)/(z1-z0)
<br>
if (z.gt.z1) scale = smax
<br>
<br>
which would yield
<br>
<br>
scale = 1 when z=z0
<br>
scale = smax when z >= z1
<br>
<br>
Paul
<br>
<br>
<br>
<br>
On Sun, 19 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi paul,
<br>
<br>
The code works fine, but there should be a
small change thats has
<br>
to be done
<br>
<br>
<br>
if (z.gt.z0) scale = 1 + (z /(z1-z0 )))
<br>
if (z.gt.z1) scale = smax
<br>
<br>
This creates a perfect diverging pipe.
<br>
<br>
Thanks for the help paul.
<br>
<br>
Kamal
<br>
<br>
On Jan 20, 2014, at 12:09 AM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi paul,
<br>
<br>
If I am not wrong,
<br>
I make a mesh with three straight pipes(
inlet, divergent,
<br>
outlet ) connected together via n2to3 so
that I know the element
<br>
connectivity places of the divergent section
(z0,z1) and use the
<br>
section what you gave
<br>
<br>
Thank you for the code
<br>
<br>
Kamal
<br>
<br>
On Jan 19, 2014, at 8:45 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
I would do the following in usrdat2():
<br>
<br>
n=nx1*ny1*nz1*nelt
<br>
<br>
do i=1,n
<br>
x=xm1(i,1,1,1)
<br>
y=ym1(i,1,1,1)
<br>
z=ym1(i,1,1,1)
<br>
scale = 1.
<br>
if (z.gt.z0) scale =
smax*(z-z0/(z1-z0)
<br>
if (z.gt.z1) scale = smax
<br>
xm1(i,1,1,1) = scale*x
<br>
ym1(i,1,1,1) = scale*y
<br>
enddo
<br>
<br>
Paul
<br>
<br>
Make certain that z1 and z0 correspond to
z values
<br>
that precisely coincide with element
interfaces.
<br>
<br>
<br>
On Sun, 19 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I looked into the Peris example but It
is so what same like
<br>
the stenosis example with a Cosine
deformation.
<br>
<br>
In my case it is a pipe with conical
divergent. I tried to
<br>
play around the variables Xm1, Ym1 and
Zm1 but the mapping
<br>
doesn't go well.
<br>
<br>
Could you please help me with this.
<br>
<br>
Thank you,
<br>
<br>
Kamal
<br>
<br>
<br>
On Jan 18, 2014, at 7:26 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I looked at the Helix and stenosis
example but they are using
<br>
cosine functions to deform
<br>
<br>
I tried to use a tangent function but
it bends the whole pipe.
<br>
<br>
I dint look at peris example .
<br>
<br>
I will take a look at it and let you
know.
<br>
<br>
Thank you
<br>
<br>
Kamal
<br>
<br>
On Jan 18, 2014, at 7:22 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
Have you looked at the peris
example? The usr file there
<br>
shows how to deform
<br>
a pipe geometry.
<br>
<br>
Paul
<br>
<br>
From:
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>]
on behalf of
<br>
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>]
<br>
Sent: Saturday, January 18, 2014
12:17 PM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe
with expansion
<br>
<br>
Dear Paul,
<br>
<br>
I tried many ways to map my straight
pipe geometry but it
<br>
does not seem to work properly
<br>
<br>
I used something like
<br>
<br>
X = X + Z * tan ( alpha )
<br>
Y = Y + Z* tan (alpha )
<br>
<br>
<br>
even that dint work. could please
help me with this
<br>
<br>
Thank you
<br>
<br>
Kamal.
<br>
<br>
On Jan 17, 2014, at 2:24 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
Thanks paul. I tried working with
the diverging mesh
<br>
modification.
<br>
<br>
I tried to use this form of
equation to modify the mesh
<br>
<br>
z = mx + b
<br>
z = ny + c
<br>
<br>
x = ( z - b ) / m
<br>
y = (z - c) / n
<br>
<br>
Do you think would work ? or is
there any other way to
<br>
input that ?
<br>
<br>
Thanks,
<br>
<br>
Kamal
<br>
<br>
<br>
On 17/01/2014 14:14,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.govwrote">nek5000-users@lists.mcs.anl.govwrote</a>:
<br>
<blockquote type="cite">Kamal,
<br>
<br>
1) To check for convergence, run
your simulation for
<br>
increasing polynomial orders (
lx1 in the SIZE file) and
<br>
measure some consistent quantity
(drag, TKE, etc). You
<br>
can plot this quantity against
lx1 and this should give
<br>
you a good picture of how you
are converging (without
<br>
needing to change the physical
mesh).
<br>
<br>
2) If you weren't using
temperature in your simulation,
<br>
you could do put the following
code snippet in your userchk
<br>
<br>
c-------------------------------------------
<br>
integer i, ntot
<br>
<br>
ntot = nx1*ny1*nz1*nelv ! total
number of points in
<br>
simulation (on THIS processor)
<br>
<br>
do i = 1,ntot
<br>
t(i,1,1,1,1) =
0.5*(vx(i,1,1,1)**2 +
vy(i,1,1,1)**2 +
<br>
vz(i,1,1,1)**2)
<br>
enddo
<br>
<br>
ifto = .true.
<br>
c-------------------------------------------
<br>
<br>
I've assumed here that your
density is unity. This
<br>
computed kinetic energy
point-wise and stores it in the
<br>
temperature field. The part
"ifto = .true." tells Nek to
<br>
output the temperature field
whenever it outputs a field
<br>
file. You could then view this
in visit just like you
<br>
would the velocity field.
<br>
<br>
Hope this helps!
<br>
<br>
Josh
<br>
<br>
<br>
<br>
<br>
<br>
On Wed, Jan 15, 2014 at 9:52 AM,
<br>
<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov"><nek5000-users@lists.mcs.anl.gov></a>
wrote:
<br>
Hi Paul,
<br>
<br>
I will try that mapping, I
created a straight pipe to do
<br>
some simulations.
<br>
<br>
1) Is there a way to check my
spectral convergence, so
<br>
that I can do some mesh
convergence study?
<br>
2) Is there a way to plot the
kinetic energy in the flow ?
<br>
<br>
Thank you,
<br>
Kamal
<br>
<br>
<br>
<br>
<br>
On 15/01/2014 12:14,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Hi Kamal,
<br>
<br>
For the geometry you describe, I
would apply mesh morphing
<br>
to a standard straight pipe.
You can create such a pipe
<br>
using a subset of the mkmesh
script provided in the expansion
<br>
example.
<br>
<br>
If your transition region is
conical, then I woud make
<br>
certain that the change in slope
occurs at element
<br>
boundaries,
<br>
i.e., as in the half
cross-section depicted below:
<br>
<br>
_______________
<br>
/|
| |
<br>
/ |
| |
<br>
/| |
| |
<br>
________________/ | |
| |
<br>
| | | | | |
| |
<br>
| | | | | |
| |
<br>
+-----+-----+---+--+---+------+------+---->
z
<br>
<br>
<br>
Paul
<br>
<br>
<br>
<br>
On Wed, 15 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Hi Paul,
<br>
<br>
I looked at the example and it
looks very helpful, but for
<br>
a sudden expansion we have only
two parts (i.e) the inlet
<br>
pipe and the outlet pipe.
Whereas in a diverging pipe we
<br>
have three section (i.e,) The
inlet pipe, Diverging
<br>
section and the outlet pipe.
<br>
<br>
<br>
Is it possible for me to create
a 2D diverging section
<br>
using mesh modification and
revolve it around the centre
<br>
axis to get a 3d diverging pipe
?
<br>
<br>
<br>
or should I apply the mesh
modification directly to the 3d
<br>
sudden expansion pipe using
usrdat2() ?
<br>
<br>
Thanks,
<br>
Kamal
<br>
<br>
<br>
On 14/01/2014 21:09,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
Hi Paul,
<br>
<br>
Thanks a lot for the update. I
will take a look at as soon
<br>
as possible and keep you updated
with it.
<br>
<br>
Thank you,
<br>
<br>
Kamal
<br>
<br>
On Jan 14, 2014, at 9:04 PM,
<br>
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Kamal,
<br>
<br>
I've added an example for a
step-type expansion in a pipe.
<br>
New example directory
<br>
is nek5_svn/examples/expansion,
with a README.
<br>
<br>
If you want a standard diffuser,
I would use
<br>
mesh-morphing, as outlined in
the
<br>
nek primer, which can be found
on this page:
<br>
<br>
<a class="moz-txt-link-freetext" href="http://nek5000.mcs.anl.gov/index.php/UG#Documentation">http://nek5000.mcs.anl.gov/index.php/UG#Documentation</a>
<br>
<br>
I've also automated our
turbulent outflow bc treatment
--
<br>
one simply provides an
<br>
expansion factor (typically ~
1.5) and two persistent
<br>
arrays to turb_outflow(), which
<br>
is now in navier5.f. This can
be useful when very
<br>
strong vortices are leaving the
<br>
domain, which is possible for
certain diffuser flow
<br>
conditions (and others).
<br>
<br>
Paul
<br>
________________________________________
<br>
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Sent: Monday, January 13, 2014
3:35 AM
<br>
To:
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: [Nek5000-users]
Creating a Mesh
<br>
<br>
Hi
<br>
<br>
Can some one please help me in
this because I am new to nek
<br>
<br>
1) How can I create a .rea for a
specific geometry say ' A
<br>
sudden
<br>
expansion pipe ' or a '
Diverging pipe '
<br>
<br>
2) What tool I should use to
create that mesh.
<br>
<br>
<br>
Thank you
<br>
<br>
<br>
kamal
<br>
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On Fri, 24 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hello Paul,
<br>
<br>
Thanks for your reply. I am looking into the .usr file for
defining the set_obj ().
<br>
<br>
1) Could you please tell me what is 'Enter the number of
levels ?' in n2to3
<br>
<br>
is it the number of elements in Z direction ?
<br>
<br>
2) As you said about storing the computed vorticity in
velocity field to view in VisIT, I found the routine to
compute the vorticity but I am stuck about adding it to the
velocity filed to VisIT ? could you please tell me how it
works or any example which stores vorticity to the .fld file
as a separate variable.
<br>
<br>
<br>
Thank you
<br>
<br>
Kamal
<br>
<br>
<br>
On 22/01/2014 16:53, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<blockquote type="cite">Axial viscous stress is given by
torq_calc -- that's no problem whatsoever. You get a number
as a
<br>
function of time.
<br>
<br>
You can even get stresses on multiple subsets of the
geometry (e.g., if you had multiple branches
<br>
in the domain or multiple cylinders. The drag, which is a
byproduct of the torque computation (which
<br>
you can ignore), is given in terms of the viscous and
pressure components separately and as the
<br>
sum of the two.
<br>
<br>
You can identify domain boundaries by checking the boundary
conditions. Here, I recommend
<br>
looking at the set_obj routines in several of the /example
cases.
<br>
<br>
<br>
________________________________________
<br>
From: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
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<br>
Sent: Wednesday, January 22, 2014 9:37 AM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe with expansion
<br>
<br>
Hello Paul
<br>
<br>
I was thinking about taking the tangential velocity near to
the wall so that I can figure out my length of the
recirculation region.
<br>
<br>
Is it possible for me to access the boundary elements of the
mesh ??? so that I can take the boundary element and then
obtain the velocity at that point so that I can figure out
the length of my recirculation region.
<br>
<br>
or take the *.fld file and read it to plot the datas I need.
<br>
<br>
<br>
I also want to calculate the axial viscous force acting on
the entire pipe.
<br>
<br>
which is given by
<br>
<br>
C_v = F^v / ( d^2 * rho * U^2 ) = double integral ( 1/Re
* (du / dr) ) dtheta dz
<br>
<br>
<br>
On Jan 22, 2014, at 4:07 PM, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
As I thought about it some more, if you're interested in
the local wall shear stress
<br>
magnitude I'm quite certain you can get this by plotting
the magnitude of vorticity
<br>
on the surface in question. (Note that the sign of the
WSS, which in fact is a tensor
<br>
or a vector when restricted to a given surface, is lost in
this process, but that might
<br>
not be relevant for your needs.) If that works, then you
can readily compute the
<br>
vorticity using one of the routines in nek and store the
result in a velocity field, then
<br>
view that field with VisIt. Of course WSS will require
multiplication by viscosity.
<br>
<br>
hth,
<br>
<br>
Paul
<br>
<br>
________________________________________
<br>
From: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
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<br>
Sent: Tuesday, January 21, 2014 10:33 AM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe with expansion
<br>
<br>
Hi paul,
<br>
<br>
can I make this to be drag or shear quantities to be
return to the a
<br>
separate file so that it will easy for me to plot.
<br>
<br>
By the way it gives the integral quantity. Think for
example I need to
<br>
find the shear stress on the wall from the inlet to
outlet at a
<br>
particular time = 2 . How can I do that ?
<br>
<br>
Is there way to find the number of elements in x,y and z
direction ?
<br>
<br>
On 21/01/2014 17:32, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
Your integrated drag quantities should be written to the
logfile
<br>
(stdout),
<br>
assuming you've set the arguments in the call to be
.true.
<br>
<br>
Paul
<br>
<br>
On Tue, 21 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I checked the set_obj subroutine and implemented one
in my .USR file.
<br>
The code seem to run without any errors but I don't
find where these
<br>
variables are getting stored.
<br>
<br>
I use VisIT to visualize my output, even there was no
change in it.
<br>
<br>
do I have to define my own output file and write the
variables out ?
<br>
<br>
Thanks,
<br>
<br>
Kamal.
<br>
<br>
<br>
On 20/01/2014 21:52, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<blockquote type="cite">Hi Kamal,
<br>
<br>
You'll need to compute your own tke by manipulating
the
<br>
velocity fields.
<br>
<br>
You can get running averages of the requisite
quantities
<br>
via calls to "avg_all" which is found in navier5.f
<br>
<br>
You can compute shear stress on the wall simply by
computing
<br>
the drag on the wall, which can be done via a call
to torque_calc(),
<br>
also found in navier5.f
<br>
<br>
If you cd to /examples and type:
<br>
<br>
grep torq */*.usr
<br>
<br>
you'll find many examples of calls to torque_calc.
You simply
<br>
need to prescribe the surfaces on which shear is to
be integrated.
<br>
<br>
I typically write a routine "set_obj" to identify
such surfaces
<br>
on the first call to usrchk.
<br>
<br>
grep set_obj */*.usr
<br>
<br>
will show similar examples.
<br>
<br>
I would recommend trying this for laminar Poiseiulle
flow in
<br>
a very simple channel just to check that your calls
are properly
<br>
set.
<br>
<br>
Best,
<br>
<br>
Paul
<br>
<br>
<br>
On Mon, 20 Jan 2014, <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
Thanks and that helped.
<br>
<br>
Where can I find the variables like Turbulent KE ,
shear stress on
<br>
the wall. ?
<br>
<br>
Do i have to activate some parameters for
calculating them ?
<br>
<br>
If I had to plot them.
<br>
<br>
Thanks,
<br>
Kamal
<br>
<br>
<br>
On Jan 20, 2014, at 5:41 AM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
Looks good.
<br>
<br>
I'm guessing that one further refinement would
be:
<br>
<br>
if (z.gt.z0) scale = 1 + (smax-1)*(z-z0)/(z1-z0)
<br>
if (z.gt.z1) scale = smax
<br>
<br>
which would yield
<br>
<br>
scale = 1 when z=z0
<br>
scale = smax when z >= z1
<br>
<br>
Paul
<br>
<br>
<br>
<br>
On Sun, 19 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi paul,
<br>
<br>
The code works fine, but there should be a
small change thats has
<br>
to be done
<br>
<br>
<br>
if (z.gt.z0) scale = 1 + (z /(z1-z0 )))
<br>
if (z.gt.z1) scale = smax
<br>
<br>
This creates a perfect diverging pipe.
<br>
<br>
Thanks for the help paul.
<br>
<br>
Kamal
<br>
<br>
On Jan 20, 2014, at 12:09 AM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi paul,
<br>
<br>
If I am not wrong,
<br>
I make a mesh with three straight pipes(
inlet, divergent,
<br>
outlet ) connected together via n2to3 so
that I know the element
<br>
connectivity places of the divergent section
(z0,z1) and use the
<br>
section what you gave
<br>
<br>
Thank you for the code
<br>
<br>
Kamal
<br>
<br>
On Jan 19, 2014, at 8:45 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
I would do the following in usrdat2():
<br>
<br>
n=nx1*ny1*nz1*nelt
<br>
<br>
do i=1,n
<br>
x=xm1(i,1,1,1)
<br>
y=ym1(i,1,1,1)
<br>
z=ym1(i,1,1,1)
<br>
scale = 1.
<br>
if (z.gt.z0) scale =
smax*(z-z0/(z1-z0)
<br>
if (z.gt.z1) scale = smax
<br>
xm1(i,1,1,1) = scale*x
<br>
ym1(i,1,1,1) = scale*y
<br>
enddo
<br>
<br>
Paul
<br>
<br>
Make certain that z1 and z0 correspond to
z values
<br>
that precisely coincide with element
interfaces.
<br>
<br>
<br>
On Sun, 19 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a> wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I looked into the Peris example but It
is so what same like
<br>
the stenosis example with a Cosine
deformation.
<br>
<br>
In my case it is a pipe with conical
divergent. I tried to
<br>
play around the variables Xm1, Ym1 and
Zm1 but the mapping
<br>
doesn't go well.
<br>
<br>
Could you please help me with this.
<br>
<br>
Thank you,
<br>
<br>
Kamal
<br>
<br>
<br>
On Jan 18, 2014, at 7:26 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
I looked at the Helix and stenosis
example but they are using
<br>
cosine functions to deform
<br>
<br>
I tried to use a tangent function but
it bends the whole pipe.
<br>
<br>
I dint look at peris example .
<br>
<br>
I will take a look at it and let you
know.
<br>
<br>
Thank you
<br>
<br>
Kamal
<br>
<br>
On Jan 18, 2014, at 7:22 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Kamal,
<br>
<br>
Have you looked at the peris
example? The usr file there
<br>
shows how to deform
<br>
a pipe geometry.
<br>
<br>
Paul
<br>
<br>
From:
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>]
on behalf of
<br>
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>]
<br>
Sent: Saturday, January 18, 2014
12:17 PM
<br>
To: <a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: Re: [Nek5000-users] Pipe
with expansion
<br>
<br>
Dear Paul,
<br>
<br>
I tried many ways to map my straight
pipe geometry but it
<br>
does not seem to work properly
<br>
<br>
I used something like
<br>
<br>
X = X + Z * tan ( alpha )
<br>
Y = Y + Z* tan (alpha )
<br>
<br>
<br>
even that dint work. could please
help me with this
<br>
<br>
Thank you
<br>
<br>
Kamal.
<br>
<br>
On Jan 17, 2014, at 2:24 PM,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
wrote:
<br>
<br>
<blockquote type="cite">Hi Paul,
<br>
<br>
Thanks paul. I tried working with
the diverging mesh
<br>
modification.
<br>
<br>
I tried to use this form of
equation to modify the mesh
<br>
<br>
z = mx + b
<br>
z = ny + c
<br>
<br>
x = ( z - b ) / m
<br>
y = (z - c) / n
<br>
<br>
Do you think would work ? or is
there any other way to
<br>
input that ?
<br>
<br>
Thanks,
<br>
<br>
Kamal
<br>
<br>
<br>
On 17/01/2014 14:14,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.govwrote">nek5000-users@lists.mcs.anl.govwrote</a>:
<br>
<blockquote type="cite">Kamal,
<br>
<br>
1) To check for convergence, run
your simulation for
<br>
increasing polynomial orders (
lx1 in the SIZE file) and
<br>
measure some consistent quantity
(drag, TKE, etc). You
<br>
can plot this quantity against
lx1 and this should give
<br>
you a good picture of how you
are converging (without
<br>
needing to change the physical
mesh).
<br>
<br>
2) If you weren't using
temperature in your simulation,
<br>
you could do put the following
code snippet in your userchk
<br>
<br>
c-------------------------------------------
<br>
integer i, ntot
<br>
<br>
ntot = nx1*ny1*nz1*nelv ! total
number of points in
<br>
simulation (on THIS processor)
<br>
<br>
do i = 1,ntot
<br>
t(i,1,1,1,1) =
0.5*(vx(i,1,1,1)**2 +
vy(i,1,1,1)**2 +
<br>
vz(i,1,1,1)**2)
<br>
enddo
<br>
<br>
ifto = .true.
<br>
c-------------------------------------------
<br>
<br>
I've assumed here that your
density is unity. This
<br>
computed kinetic energy
point-wise and stores it in the
<br>
temperature field. The part
"ifto = .true." tells Nek to
<br>
output the temperature field
whenever it outputs a field
<br>
file. You could then view this
in visit just like you
<br>
would the velocity field.
<br>
<br>
Hope this helps!
<br>
<br>
Josh
<br>
<br>
<br>
<br>
<br>
<br>
On Wed, Jan 15, 2014 at 9:52 AM,
<br>
<a class="moz-txt-link-rfc2396E" href="mailto:nek5000-users@lists.mcs.anl.gov"><nek5000-users@lists.mcs.anl.gov></a>
wrote:
<br>
Hi Paul,
<br>
<br>
I will try that mapping, I
created a straight pipe to do
<br>
some simulations.
<br>
<br>
1) Is there a way to check my
spectral convergence, so
<br>
that I can do some mesh
convergence study?
<br>
2) Is there a way to plot the
kinetic energy in the flow ?
<br>
<br>
Thank you,
<br>
Kamal
<br>
<br>
<br>
<br>
<br>
On 15/01/2014 12:14,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Hi Kamal,
<br>
<br>
For the geometry you describe, I
would apply mesh morphing
<br>
to a standard straight pipe.
You can create such a pipe
<br>
using a subset of the mkmesh
script provided in the expansion
<br>
example.
<br>
<br>
If your transition region is
conical, then I woud make
<br>
certain that the change in slope
occurs at element
<br>
boundaries,
<br>
i.e., as in the half
cross-section depicted below:
<br>
<br>
_______________
<br>
/|
| |
<br>
/ |
| |
<br>
/| |
| |
<br>
________________/ | |
| |
<br>
| | | | | |
| |
<br>
| | | | | |
| |
<br>
+-----+-----+---+--+---+------+------+---->
z
<br>
<br>
<br>
Paul
<br>
<br>
<br>
<br>
On Wed, 15 Jan 2014,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Hi Paul,
<br>
<br>
I looked at the example and it
looks very helpful, but for
<br>
a sudden expansion we have only
two parts (i.e) the inlet
<br>
pipe and the outlet pipe.
Whereas in a diverging pipe we
<br>
have three section (i.e,) The
inlet pipe, Diverging
<br>
section and the outlet pipe.
<br>
<br>
<br>
Is it possible for me to create
a 2D diverging section
<br>
using mesh modification and
revolve it around the centre
<br>
axis to get a 3d diverging pipe
?
<br>
<br>
<br>
or should I apply the mesh
modification directly to the 3d
<br>
sudden expansion pipe using
usrdat2() ?
<br>
<br>
Thanks,
<br>
Kamal
<br>
<br>
<br>
On 14/01/2014 21:09,
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
Hi Paul,
<br>
<br>
Thanks a lot for the update. I
will take a look at as soon
<br>
as possible and keep you updated
with it.
<br>
<br>
Thank you,
<br>
<br>
Kamal
<br>
<br>
On Jan 14, 2014, at 9:04 PM,
<br>
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
wrote:
<br>
<br>
Kamal,
<br>
<br>
I've added an example for a
step-type expansion in a pipe.
<br>
New example directory
<br>
is nek5_svn/examples/expansion,
with a README.
<br>
<br>
If you want a standard diffuser,
I would use
<br>
mesh-morphing, as outlined in
the
<br>
nek primer, which can be found
on this page:
<br>
<br>
<a class="moz-txt-link-freetext" href="http://nek5000.mcs.anl.gov/index.php/UG#Documentation">http://nek5000.mcs.anl.gov/index.php/UG#Documentation</a>
<br>
<br>
I've also automated our
turbulent outflow bc treatment
--
<br>
one simply provides an
<br>
expansion factor (typically ~
1.5) and two persistent
<br>
arrays to turb_outflow(), which
<br>
is now in navier5.f. This can
be useful when very
<br>
strong vortices are leaving the
<br>
domain, which is possible for
certain diffuser flow
<br>
conditions (and others).
<br>
<br>
Paul
<br>
________________________________________
<br>
From:
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users-bounces@lists.mcs.anl.gov">nek5000-users-bounces@lists.mcs.anl.gov</a>]
on behalf
<br>
<a class="moz-txt-link-abbreviated" href="mailto:ofnek5000-users@lists.mcs.anl.gov">ofnek5000-users@lists.mcs.anl.gov</a>
<br>
[<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>]
<br>
Sent: Monday, January 13, 2014
3:35 AM
<br>
To:
<a class="moz-txt-link-abbreviated" href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
<br>
Subject: [Nek5000-users]
Creating a Mesh
<br>
<br>
Hi
<br>
<br>
Can some one please help me in
this because I am new to nek
<br>
<br>
1) How can I create a .rea for a
specific geometry say ' A
<br>
sudden
<br>
expansion pipe ' or a '
Diverging pipe '
<br>
<br>
2) What tool I should use to
create that mesh.
<br>
<br>
<br>
Thank you
<br>
<br>
<br>
kamal
<br>
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<br>
<br>
"All that is necessary for the
triumph of evil is that
<br>
good men do nothing" -- Edmund
Burke
<br>
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Nek5000-users mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Nek5000-users@lists.mcs.anl.gov">Nek5000-users@lists.mcs.anl.gov</a>
<a class="moz-txt-link-freetext" href="https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users">https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users</a>
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