[Nek5000-users] turbulent 3d box

Sun Dec 22 16:25:16 CST 2013

It didn't work (I tried both options). Do you have working example?
(see my previous email and my attachment).
Barak

On 12/22/2013 11:20 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> 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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>>>>>
>>>>> <UrlBlockedError.aspx>
>>>>
>>>>
>>>>
>>>>
>>>>
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>>>
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