[Nek5000-users] Questions in AXHELM and WLAPLACIAN

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

Hi Paul,

Thank you for your quick answer, this is really helpful.

I still have a question concerning the computation of a gradient.

Why did you construct the diffusion operator with the helmholtz routine? Why not using directly the routines gradm1 ?


By the way I am not sure to understand the differences between gradm1 (navier5.f), wgradm1 (navier1.f) , gradm11 (navier2.f) and gradm11ts (navier2.f).
I guess that the w letter refers to the weak formulation, but I don’t understand in which cases we need to choose a formulation instead of others.

In summary, if I want to modify the temperature/passive scalar equations to add a term that contains a gradient of the solved temperature/PS variable, for example, which “gradm” routine do I need to use?

Thank you for your help !


Best regards,
Emmanuel



On 29 May 2014, at 20:20, nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov> wrote:



Hi Emmanuel,

axhelm effects the weak Laplacian plus the mass matrix.

Specifically, if you wanted to solve:

(1)   -nabla . [ h1 * nabla ] u + h2 * u   =  f

with h1, h2, and f all functions of X=(x,y,z),
the discrete form would be:


(2)         A(h1) u + B(h2) u = B f

or

(3)         H u = B f

where A is the (h1-dependent stiffness matrix and
B(h2) is the h2-dependent mass matrix.

For the SEM, B is diagonal, so B(h2) = h2*B, where
we view h2 as a diagonal matrix.

In Nek5000, a matrix-vector product  w = Hu is effected via

     call axhelm (w,u,h1,h2,imesh,isd)

with w,u,h1,h2 being arrarys.   Here, imesh indicates
if you are on the fluid mesh or thermal mesh.  The fluid
mesh is a subset of the thermal mesh in the case of conjugate heat transfer between a fluid and a solid.
isd indicates which spatial direction is considered
in axisymmetric applications where u is a component
of a vector field.

Notice the sign of the Laplacian in Eq. (1) -- that may
help resolve your second question?  (There is a sign
change that ariss from the standard integration-by-parts
stepin the weak form.)

Paul


On Thu, 29 May 2014, nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov> wrote:

Dear nek5000 team,

Could you help me with the 2 questions below? Thank you very much !

1) Concerning the routine “axhelm” in hmholtz.f. If I am right, one
possibility of this routine can be the discretisation of the diffusion
operator. However it is not clear to me if axhelm performs:

a) vdiff  x   Laplacian(phi)

or

b) grad ( vdiff x grad (phi) )

phi being the variable solved for (T or PS for example).

So, is it actually a) or b) ?


2) In the routine wlaplacian in navier1.f, I am not sure to understand the
consequence of the line:

call sub2 (out,wrk,ntot)

after the lines:

call bcneusc(out,1) call axhelm(wrk,a,diff,h2,imesh,1)

If I am right, this will change the sign in front of the diffusion operator,
right?  Because in makeq.f, I am not sure that the line call
add2(bq(1,1,1,1,ifield-1),w1,ntot)

will actually assemble the RHS of the transport equation :  - (vtrans) x  U
grad (phi)  +  grad ( vdiff x grad (phi) )


Thank you for your help !

Best regards, Emmanuel

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