[Getdp] Laplace problem, Dirichlet and Neumann condition.

[François Henrotte]

Hello Isabel,

it seems to me that the model is correct
and that the Neumann B.C. is correctly taken into account.

The formulation, however is a bit unusual.

As you did not say what application it is,
I shall assume it be a thermal problem.

The Dirichlet B.C. on the side of the cylinder
imposes a normal/radial heat flux.
The Neumann B.C. on the planar faces,
on the other hand,
imposes an axial heat flux (in X direction).
The two B.C’s are thus kind of contradictory
on the edges of the cylindre,
hence the strange looking of the computed gradient of temperature (ValueDNVolume).

Note also that the PostProcessing quantity

 { Name ValueDNSurfaces; Value { Local { [ {d N} ]; In Superficies; Jacobian Sur; Integration Int;} } }

only returns the tangential part of the gradient
(the one that lives in the surface).
This might be the reason why you felt
the Neumann B.C. was not taken into consideration.

Hope this helps,

Fr.


Le 10 oct. 2019 à 13:59, Isabel Martínez <isabelXXI21 at hotmail.com<mailto:isabelXXI21 at hotmail.com>> a écrit :

Dear all:

This is the first time I am using getdp. I am trying to solve a Laplace problem with mixed boundary conditions in a cylinder. The equations are:

- Laplacian N = 0 inside the cylinder.

N = 0 on the side of the cylinder.
grad N * normal[] = - CompX[Normal[]] on the bases of the cylinder.

I have my .geo and .pro files, but when getdp computes the solution the Neumann condition is not fulfilled. I checked the normal vectors with the gui of gmsh and the postprocesing of getdp and they looked good. I tried with different ways of define my geometry but it gives me the same results.

I put the Dirichlet condition as a constraint and the weak formulation is:
[Dof{d N} ,{d N} ]_inside the cylinder
+ [CompX[Normal[]] ,{N} ]_on the bases of the cylinder.

I am using getdp-3.2.0 and gmsh-4.4.1 for Windows64. I also tried with the version from the 1st of October of 2019 of ONELAB.

I can't find what is wrong, I would be thankful if someone can help me. I attached the .geo and .pro files.

Thank you in advance.
Isabel.

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François Henrotte Dr Ir - francois.henrotte at uclouvain.be<mailto:francois.henrotte at uclouvain.be> - francois.henrotte at uliege.be<mailto:francois.henrotte at uliege.be>
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