[Nek5000-users] turbulent 3d box

Sun Dec 22 15:14:59 CST 2013

Hi Barak,

You can either increase lx1,ly1, lz1 in SIZE and re-make, or you
can change nelx,nely,nelz in the .box file.

Did you resolve the issue with the initial condition?

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, December 22, 2013 3:05 PM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] turbulent 3d box

Hi Paul,
Before I run problems with smaller viscosity: how I increase the
resolution? and remesh the box?
Barak

On 12/22/2013 10:24 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> Hi Barak,
>
> When I compute the L2 norm of the function, given as:
>
>         v2 = [ sum_i  vx_i b_i vx_i + vy_i b_i vy_i + vz_i b_i vz_i / sum_i b_i ]^(1/2)
>
> it comes out to ~ 2.23
>
> Note that there are some places where ux==2, uy==0, uz==1,
> which would give an L2 norm of
>
>       sqrt (2*2 + 0*0 + 1*1) = sqrt(5) > sqrt(3)
>
> ?
>
> 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, December 22, 2013 11:04 AM
> To: nek5000-users at lists.mcs.anl.gov
> Subject: Re: [Nek5000-users] turbulent 3d box
>
> Hi Paul,
> My definition for velocity magnitude is:
> |v|=sqrt(ux^2+uy^2+uz^2)
> so if you see, there are two components in the form:
> cos^2(x)+sin^2(x)
> etc in each direction
> so in fact
> |v|=sqrt(3) for any x,y,z.
> Isn't correct?
> Barak
>
> On 12/22/2013 05:05 PM, nek5000-users at lists.mcs.anl.gov wrote:
>>
>> Hi Barak,
>>
>> If your initial condition is:
>>
>>         ux=(cos(y)+sin(z))
>>         uy=(cos(z)+sin(x))
>>         uz=(cos(x)+sin(y))
>>
>> and your domain is [0,2pi]^3, how is it possible that your velocity
>> magnitude
>> is less than 2?
>>
>>
>> What is your measure of velocity magnitude?   When I compute the L2
>> norm of this initial condition I'm seeing about 2.3+
>>
>> 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, December 22, 2013 7:53 AM
>> *To:* nek5000-users at lists.mcs.anl.gov
>> *Subject:* Re: [Nek5000-users] turbulent 3d box
>>
>> Hi Paul,
>> It seems that something does not work, comparing my simulations using a
>> standard spectral code (pseudo-spectral). For nu=0.1, I used 16 points
>> for each space direction. Now for this case, the nonlinear terms vanish
>> (just cancel each other) and the solution is just the ABC flow if you
>> set it as initial condition. Then since the forcing is f=nu*ABC the
>> dissipation term (Laplacian) dissipation=-nu*ABC and therefore the
>> initial value (ABC) remains as it is. If we decrease the viscosity above
>> the critical value of 1/12 (if I remember correctly) there is a
>> bifurcation (Hopf...) and we obtain a new periodic solution (in time),
>> where the ABC modes are dominating combined with some high wave numbers
>> that are oscillating.
>>
>>   >From my first tests using NEK, I find that the velocity field (for
>> nu>1/12) does not agree with the above characteristics. For example, the
>> max magnitude of the velocity field should be for the ABC flow sqrt(3),
>> whereas here I get a value close to 2.5.
>>
>> Do you have any idea what's wrong?
>> If you wish to read some literature about the ABC flow as a forcing for
>> Navier Stokes or as a prescribed velocity for generation of magnetic
>> field (i.e., kinematic generation of magnetic field MHD):
>>
>> 1. D. Galloway and U. Frisch. A numerical investigation of magnetic
>> field generation in a flow with chaotic streamlines. Geophysical &
>> Astrophysical Fluid Dynamics, 29(1):13–18, 1984.
>>
>> 2. D. Galloway and U. Frisch. Dynamo action in a family of flows with
>> chaotic streamlines.
>> Geophysical & Astrophysical Fluid Dynamics, 36(1):53–83, 1986.
>>
>> 3. Podvigina, Pouquet, On the non-linear stability of the 1:1:1 ABC flow,
>> Phys. D, Vol. 75, 4, 1994.
>>
>>
>> With my best wishes,
>> Barak
>>
>>
>> Quoting nek5000-users at lists.mcs.anl.gov
>> <mailto:nek5000-users at lists.mcs.anl.gov>:
>>
>>> Hi Barak,
>>>
>>> Thanks for the note about the ABC flow -- that's very useful.
>>>
>>> What is your target viscosity?
>>> If you want it to be 0.1, then you would set param 2 in the .rea file
>>> to be 0.1.
>>> Setting param 2 = -0.1 would imply that Re=0.1 or equivalently nu=10.
>>> Does this resolve the issue for you?
>>>
>>> Once it's working we could add it as a documented example in the example
>>> suite.
>>>
>>> Thanks!
>>>
>>> Paul
>>> ________________________________________
>>> From: nek5000-users-bounces at lists.mcs.anl.gov
>>> <mailto:nek5000-users-bounces at lists.mcs.anl.gov>
>>> [nek5000-users-bounces at lists.mcs.anl.gov
>>> <mailto:nek5000-users-bounces at lists.mcs.anl.gov>] on behalf of
>>> nek5000-users at lists.mcs.anl.gov
>>> <mailto:nek5000-users at lists.mcs.anl.gov>
>>> [nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov>]
>>> Sent: Saturday, December 21, 2013 5:24 PM
>>> To: nek5000-users at lists.mcs.anl.gov
>>> <mailto:nek5000-users at lists.mcs.anl.gov>
>>> Subject: Re: [Nek5000-users] turbulent 3d box
>>>
>>> Hi Paul,
>>> Regarding the 3dbox:
>>> The forcing which I propose is known as the ABC flow
>>> (Arnold-Beltrami-Childress) and has steady solutions (in the form of ABC
>>> flow) with Re=1/nu (nu the viscosity) Re=<12 (in periodic box).
>>> The forcing should be in the form:
>>> f=Re*ABC in order to balance the dissipation term.
>>> This settings can serve as a benchmark for pure hydro/mhd problems.
>>>
>>> I tried to fix the example which you have sent me, but I don't succeed
>>> retreiving the expected values.
>>> I attach the relevant files( tarball file).
>>> Best regards,
>>> Barak
>>>
>>>
>>>
>>> On 12/18/2013 03:29 AM, nek5000-users at lists.mcs.anl.gov
>>> <mailto:nek5000-users at lists.mcs.anl.gov> wrote:
>>>
>>>> Hi Barak,
>>>>
>>>> I added a 3d periodic box under "3dbox" in the examples
>>>> directory.
>>>>
>>>> Paul
>>>>
>>>>
>>>> Dear nek's,
>>>> I would like to run the following problem:
>>>> a 3D periodic box, small viscosity and the following forcing:
>>>>
>>>> fx=cos(y)+sin(z)
>>>> fy=cos(z)+sin(x)
>>>> fz=cos(x)+sin(y)
>>>>
>>>> Do you have a similar example?
>>>>
>>>> Many thanks,
>>>> Barak
>>>>
>>>>
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>>
>>
>>
>>
>>
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