[Nek5000-users] Calculation of Divergence Term
nek5000-users at lists.mcs.anl.gov
nek5000-users at lists.mcs.anl.gov
Sat Nov 12 11:26:11 CST 2011
No problem... sorry for the delay in getting you what you needed.
On Sat, 12 Nov 2011, nek5000-users at lists.mcs.anl.gov wrote:
> Hi,
>
> Thanks a lot for your hints and I appreciate your help. Sorry for
> interrupting when you were so busy.
>
> Regards,
> Alireza Karimi
>
>
>
>
> Quoting nek5000-users at lists.mcs.anl.gov:
>
>>
>> Dear Alireza,
>>
>> You would add this to qvol, since it is the convection-diffusion
>> equation -- so, the routine is userq.
>>
>> You should precompute the term in userchk, store the result in
>> a common block, and then dereference in userq. Expanding on Josh's
>> suggestion below you would have something like
>>
>> c-----------------------------------------------------------------------
>> subroutine userchk
>> :
>> :
>>
>> common /mydiv/ divcv(lx1,ly1,lz1,lelt)
>> common /scrns/ dcv1dx(lx1,ly1,lz1,lelt)
>> , dcv2dy(lx1,ly1,lz1,lelt)
>> , dcv3dz(lx1,ly1,lz1,lelt)
>> , work1 (lx1,ly1,lz1,lelt)
>> , work2 (lx1,ly1,lz1,lelt)
>>
>>
>> then his calls... be sure to define n
>>
>> return
>> end
>> c-----------------------------------------------------------------------
>> subroutine userq (ix,iy,iz,eg)
>> include 'SIZE'
>> include 'TOTAL'
>> include 'NEKUSE'
>>
>> common /mydiv/ divcv(lx1,ly1,lz1,lelt)
>>
>> integer e,f,eg
>> e = gllel(eg)
>>
>> qvol = divcv(ix,iy,iz,e) Be sure to check the sign of this term
>>
>> return
>> end
>> c-----------------------------------------------------------------------
>>
>>
>>
>> It's not a priori clear that you need to dealias this term.
>> Dealiasing is needed in certain circumstance for stability -- it
>> does not materially affect accuracy. Without further context
>> I cannot tell you whether you need to dealias or not.
>>
>> The approach suggested by Josh is perfectly adequate for the
>> standard (non-dealiased) approach.
>>
>>
>> Paul
>>
>>
>> On Fri, 11 Nov 2011, nek5000-users at lists.mcs.anl.gov wrote:
>>
>>> Hi,
>>>
>>> I'm sending this message again, because I got no answer for my last email.
>>> I have some questions regarding the additional term given in my previous
>>> message. I don't know where and in which subroutine I should add this term
>>> to the right hand side of the advection-diffusion equation. Also, could
>>> you please provide me with the best option I can take to dealias this term
>>> (if needed at all)? I wonder if you could help me in this regard.
>>>
>>> Best Regards,
>>> Alireza Karimi
>>>
>>>
>>>
>>> Quoting nek5000-users at lists.mcs.anl.gov:
>>>
>>>> Alireza,
>>>>
>>>> For this, I'll assume that you have split V into V1, V2, V3, and that
>>>> they have the structure
>>>>
>>>> V1(lx1,ly1,lz1,lelv) (and likewise for the other two)
>>>>
>>>>
>>>> First, to multiply c*V1 (V2, V3), you can use col2. It would look like
>>>>
>>>> call col2(V1,c,n)
>>>> call col2(V2,c,n)
>>>> call col2(V3,c,n)
>>>>
>>>> where n = nx1*ny1*nz1*nelv. A couple of things to note here:
>>>>
>>>> 1) col2 will overwrite V1 (V2, V3). Effectively, the operation is
>>>> V1 = c*V1. If this is not desirable, then you could use col3 with
>>>> something like
>>>>
>>>> call col3(cV1,V1,c,n)
>>>>
>>>> This will store it in cV1 and leave V1 untouched.
>>>>
>>>> 2) You could run into aliasing issues by multiplying c and V
>>>> directly, and so it may be wise to dealias the product before taking
>>>> the derivative. Developers, maybe you could suggest the best way of
>>>> going about doing this in Nek???
>>>>
>>>> Moving on, to take the derivatives, there are a few choices. One way
>>>> would be do to something like
>>>>
>>>> call gradm1(dcV1dx,work1 ,work2 ,cV1)
>>>> call gradm1(work1 ,dcV2dy,work2 ,cV2)
>>>> call gradm1(work1 ,work2 ,dcV3dz,cV3)
>>>>
>>>> call add4(divcV, dcV1dx, dcV2dy, dcV3dz, n)
>>>>
>>>> which would give you div(cV) in the array divcV. Note that dcV1dx,
>>>> dcV2dy, dcV3dz, work1, work2, and divcV all should have the same
>>>> storage structure as V1, c, etc.
>>>>
>>>> This is probably the simplest way that I can think to do it, although
>>>> it is somewhat inefficient since we are computing, for instance,
>>>> d(cV1)/dy unnecessarily. To make it more efficient, you can manually
>>>> compute the derivatives individually (take a look at the gradm1
>>>> subroutine to get an idea of how to do this, located in navier5.f in
>>>> the source)
>>>>
>>>> Hope this helps, and developers, please correct me if I did something
>>>> horribly wrong here :).
>>>>
>>>> Josh
>>>>
>>>> On Fri, Nov 4, 2011 at 4:59 PM, <nek5000-users at lists.mcs.anl.gov> wrote:
>>>>> Hi,
>>>>>
>>>>> I want to solve an advection-diffusion equation in conjunction with the
>>>>> momentum and mass conservation equations. But my equation has an extra
>>>>> divergence term which I don't know how to calculate it in Nekton. So,
>>>>> denoting the scalar concentration field with c and velocity field with
>>>>> u,
>>>>> the equation turns out to be:
>>>>>
>>>>> dc/dt + u.grad c = Laplacian c - div (c V)
>>>>>
>>>>> which by d/dt I mean partial derivative with respect to time. V is a
>>>>> known
>>>>> vector field calculated from the vorticity tensor. I wonder if you could
>>>>> show me how to evaluate this additional term (the last term) in the user
>>>>> file.
>>>>>
>>>>>
>>>>> Best Regards,
>>>>> Alireza Karimi
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Nek5000-users mailing list
>>>>> Nek5000-users at lists.mcs.anl.gov
>>>>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Josh Camp
>>>>
>>>> "All that is necessary for the triumph of evil is that good men do
>>>> nothing" -- Edmund Burke
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>>>
>>>
>>>
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