[Nek5000-users] Constant mass flow rate in simulation

Mon Sep 1 16:14:40 CDT 2014

Hi Tony,

Nek uses a semi-implicit formulation in which the nonlinear term
is treated explicitly in time.

The update is of the form:

(1)   L(U,p) = NL(u) + BC + F(t)

where, L is the linear unsteady Stokes operator, NL() accounts for
nonlinear terms and BC accounts for boundary data and F(t) accounts
for body force.   A fixed flow rate implies that F(t) adjusts to
ensure the constant flow rate.

Because L is linear, we can split the time advancement into two
parts using superposition:

(2)   L(U',p') = NL(u) + BC

(3)   L(U0,p0) = F0 + BC(0),   where BC(0) := homogeneous boundary 
conditions

(4)   U = U' + a*U0,
(5)   p = p' + a*p

where a is a constant

For fixed flow rate, you need

(6)   \int U.x_hat dV = constant

which implies

(7)   a = [ constant - \int U'.x_hat dV ] / [ \int U0.x_hat dV ]

Note that (2) is independent of U and time and therefore can
be solved in a preprocessing step (assuming dt is fixed and viscosity
is time-invariant).

That is what the vol_flow routines do.

The scheme inherits the full temporal and spatial accuracy of the
constant pressure-drop case.

hth,

Paul

On Mon, 1 Sep 2014, nek5000-users at lists.mcs.anl.gov wrote:

> Dear Paul,
>
> Thank you very much for the tips. I've tested my simulation case based on
> your instruction and it worked perfectly for keeping constant mass flow rate.
> However, I noticed that in the end of subroutine 'vol_flow', the velocity and
> pressure filed are forced to achieve constant flow rate. By doing this, would
> it be like changing the resolved flow field to get fixed flow rate, in which
> case the flow field is scaled on purpose rather than being solved directly
> from N-S equations. I don't know whether my understanding of this procedure
> is right or not. Please point out if I was wrong.
>
> Another thing is, in turbulent channel flow, in theory the constant mass flow
> rate can be achieved by balancing the force (mean pressure gradient) with
> mean wall shear stress, however this didn't work in my case. Is it because
> this method is not compatible with spectral method or is there any systematic
> issue?
>
> It would be great if you can give me some clues for my confusions. I really
> appreciate it. Thank you very much in advance.
>
> Best regards, Tony
>
> ________________________________________ From:
> nek5000-users-bounces at lists.mcs.anl.gov
> <nek5000-users-bounces at lists.mcs.anl.gov> on behalf of
> nek5000-users-request at lists.mcs.anl.gov
> <nek5000-users-request at lists.mcs.anl.gov> Sent: 01 September 2014 18:00 To:
> nek5000-users at lists.mcs.anl.gov Subject: Nek5000-users Digest, Vol 67, Issue
> 1
>
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>
>   1. Re: Outpost question (nek5000-users at lists.mcs.anl.gov) 2. Constant mass
>   flow rate in simulation (nek5000-users at lists.mcs.anl.gov) 3. Re: Constant
>   mass flow rate in simulation (nek5000-users at lists.mcs.anl.gov)
>
>
> ----------------------------------------------------------------------
>
> Message: 1 Date: Sun, 31 Aug 2014 20:17:18 +0200 From:
> nek5000-users at lists.mcs.anl.gov To: Nek 5000
> <nek5000-users at lists.mcs.anl.gov> Subject: Re: [Nek5000-users] Outpost
> question Message-ID:
> <mailman.4827.1409509062.3424.nek5000-users at lists.mcs.anl.gov> Content-Type:
> text/plain; charset="utf-8"
>
> Hi Katherine,
>
> I was wondering if you had time to check on the parameter to be reset so that
> I can overwrite previous files?
>
> Bonne soir?e, JC
>
>
> 2014-08-15 16:57 GMT+02:00 <nek5000-users at lists.mcs.anl.gov>:
>
>> Hi Katherine,
>>
>> Thanks for the answer. I knew about the parameter 15 and was not sure about
>> the 64 bits precision. This is now more clear.  Regarding the overwriting, I
>> had guessed that prepost has a parameter that needs to be reset, but I
>> haven't been able to figure out which one so far.  That would be very
>> helpful if you can take a quick look at it.
>>
>> Thanks a lot and enjoy the end of the summer ++
>>
>> JC
>>
>>
>> 2014-08-15 16:53 GMT+02:00 <nek5000-users at lists.mcs.anl.gov>:
>>
>>> Hi JC,
>>>
>>> You should be able to control the outpost frequency and precision using the
>>> parameters parameter 15 (IOSTEP) and parameter 63, respectively.
>>>
>>> So, if you wanted the first 100 steps to output every step, you would set
>>> something like:
>>>
>>> if(istep.le.100)  param(15)=1
>>>
>>>  To set the precision to 64bit, set param(63)=8, as well.  Setting
>>>  param(63) to anything else should default it to 8 byte precision.
>>>
>>> As far as overwriting previous fld files, you should be able to reset a
>>> parameter used in prepost.f that increments the file counter.  I haven't
>>> had a chance to test this, but I can take a look at it last this weekend.
>>>
>>> hth.  Katherine
>>>
>>>
>>> On Fri, Aug 15, 2014 at 3:34 AM, <nek5000-users at lists.mcs.anl.gov> wrote:
>>>
>>>> Howdy Nek's,
>>>>
>>>> I have a couple questions regarding the ouput of files:
>>>>
>>>>    1. How can force, within the code (say in usrchk), some files to be
>>>>    output in 64 bits for high-accuracy checkpointing and other in regular
>>>>    8 bits for simple visualisation?  2. Say, during the first 1000
>>>>    iterations, the code outpost a file every single iteration so that I
>>>>    have blah0.f00001 to blah0.f01000. How can I then force the code to
>>>>    outpost my new files (from istep = 1001 to 2000 say) rewriting on
>>>>    blah0.f00001 to blah0.f01000?
>>>>
>>>> Thanks a lot.  Regards,
>>>>
>>>> JC
>>>>
>>>> -- Jean-Christophe Loiseau Homepage
>>>> <https://sites.google.com/site/loiseaujc/>
>>>>
>>>> _______________________________________________ Nek5000-users mailing list
>>>> Nek5000-users at lists.mcs.anl.gov
>>>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>>>
>>>>
>>>
>>> _______________________________________________ Nek5000-users mailing list
>>> Nek5000-users at lists.mcs.anl.gov
>>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>>
>>>
>>
>>
>> -- Jean-Christophe Loiseau Homepage
>> <https://sites.google.com/site/loiseaujc/>
>>
>> _______________________________________________ Nek5000-users mailing list
>> Nek5000-users at lists.mcs.anl.gov
>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>
>>
>
>
> -- Jean-Christophe Loiseau Homepage
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> Message: 2 Date: Sun, 31 Aug 2014 22:57:27 +0000 From:
> nek5000-users at lists.mcs.anl.gov To: "nek5000-users at lists.mcs.anl.gov"
> <nek5000-users at lists.mcs.anl.gov> Subject: [Nek5000-users] Constant mass flow
> rate in simulation Message-ID:
> <mailman.4832.1409525852.3424.nek5000-users at lists.mcs.anl.gov> Content-Type:
> text/plain; charset="iso-8859-1"
>
> Dear Neks,
>
> Recently I've been struggling with constant mass flow rate in my turbulent
> channel flow simulation. Based on the userchk subroutine in 'turbChannel'
> tutorial case, I also used torque_calc(1.0,x0,.false.,.false.) to calculate
> the wall shear and then got the mean wall shear. After that I set mean
> pressure gradient 'ffx' equal to the mean wall shear in order to keep
> constant mass flow rate. In this case, the flow rate started from 1
> (nondimensionalised case, bulk mean equal to 1) and kept increasing. Although
> the increment was very small at each time step, it never stopped and the bulk
> mean velocity has increased to 1.002.
>
> Is it appropriate to set constant mass flow rate by updating mean pressure
> gradient based on mean wall shear in Nek5000 or am I using the wrong
> calculation? Since the bulk mean is still increasing, the simulation is like
> acceleration channel flow.
>
> Does anyone has any clue about how to set constant mass flow rate for
> turbulent channel flow in Nek5000? Any idea is appreciated and many thanks in
> advance.
>
> Thanks and regards, Tony
>
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> Message: 3 Date: Sun, 31 Aug 2014 23:58:32 +0000 From:
> nek5000-users at lists.mcs.anl.gov To: "nek5000-users at lists.mcs.anl.gov"
> <nek5000-users at lists.mcs.anl.gov> Subject: Re: [Nek5000-users] Constant mass
> flow rate in simulation Message-ID:
> <mailman.4833.1409529514.3424.nek5000-users at lists.mcs.anl.gov> Content-Type:
> text/plain; charset="iso-8859-1"
>
>
> Hi Tony,
>
> I would just set p55=1.0; p54=-1.0
>
> This will fix < u_x > == 1.0
>
> If you are using variable viscosity, this might be problematic, but for the
> constant viscosity case this is the best way.
>
> Be certain to also set ffx=ffy=ffz=0 in the .usr file, the the p54/p55
> combination sets the x-body force as needed to ensure the prescribed mass
> flux is realized.
>
> Paul
>
> ________________________________ From:
> nek5000-users-bounces at lists.mcs.anl.gov
> [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of
> nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov] Sent:
> Sunday, August 31, 2014 5:57 PM To: nek5000-users at lists.mcs.anl.gov Subject:
> [Nek5000-users] Constant mass flow rate in simulation
>
> Dear Neks,
>
> Recently I've been struggling with constant mass flow rate in my turbulent
> channel flow simulation. Based on the userchk subroutine in 'turbChannel'
> tutorial case, I also used torque_calc(1.0,x0,.false.,.false.) to calculate
> the wall shear and then got the mean wall shear. After that I set mean
> pressure gradient 'ffx' equal to the mean wall shear in order to keep
> constant mass flow rate. In this case, the flow rate started from 1
> (nondimensionalised case, bulk mean equal to 1) and kept increasing. Although
> the increment was very small at each time step, it never stopped and the bulk
> mean velocity has increased to 1.002.
>
> Is it appropriate to set constant mass flow rate by updating mean pressure
> gradient based on mean wall shear in Nek5000 or am I using the wrong
> calculation? Since the bulk mean is still increasing, the simulation is like
> acceleration channel flow.
>
> Does anyone has any clue about how to set constant mass flow rate for
> turbulent channel flow in Nek5000? Any idea is appreciated and many thanks in
> advance.
>
> Thanks and regards, Tony
>
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