[Nek5000-users] Calculation of Divergence Term

[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