[Nek5000-users] turbulent 3d box

Sun Dec 22 15:20:31 CST 2013

Hi Paul,
On 12/22/2013 11:14 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> 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.
>
Thanks.
> Did you resolve the issue with the initial condition?
>
See my previous email. I have inside further questions.
Best regards,
Barak


> 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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