[Nek5000-users] Calculation of Divergence Term
nek5000-users at lists.mcs.anl.gov
nek5000-users at lists.mcs.anl.gov
Mon Nov 14 20:33:57 CST 2011
Hi Neks,
Considering the advection-diffusion equation discussed in my previous
messages, I want to impose a mixed type of boundary condition for the
concentration c. In general, on the boundaries, this BC takes the
following form as,
dc/dn = (u.n + V.n)*c
where n is the normal vector to the boundary, u is the velocity field,
and V is the given vector field. I wonder if you have any idea how to
impose this mixed Dirichlet-Neumann BC in the usr file.
Regards,
Alireza Karimi
Quoting nek5000-users at lists.mcs.anl.gov:
>
> 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
>>>>>>
>>>>>>
>>>>>> _______________________________________________
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>>>>>> 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
>>>>> _______________________________________________
>>>>> Nek5000-users mailing list
>>>>> Nek5000-users at lists.mcs.anl.gov
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>>>>>
>>>>
>>>>
>>>>
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