[Nek5000-users] Calculation of Divergence Term

[nek5000-users at lists.mcs.anl.gov]

Hi,

Thank a lot for your useful hints. I have another question regarding  
this additional term. I don't know where and in which subroutine I  
should add this term to the right hand side of the advection-diffusion  
equation. I wonder if you could help me in this regard as well.

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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>
>
>
> --
> Josh Camp
>
> "All that is necessary for the triumph of evil is that good men do
> nothing" -- Edmund Burke
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