Geordie McBain wrote:
Hello. I'd like to calculate the integrated flux of a vector field
through a patch on the boundary. For example, after solving say a
Laplace equation for temperature, I'd take the gradient of the
temperature, and integrate the normal component of that over some part
of the boundary (a Physical Surface in 3-D or Physical Line in 2-D)
over which I'd specified the temperature with a Dirichlet condition in
order to get the heat transfer rate.
I read that Plugin(Integrate) `integrates...the circulation/flux of
vector fields over line/surface elements', so that looks ideal, but I
guess I'm not calling it correctly.
For example (to avoid posting a lengthy data file) say I load the
tutorial t7.geo, then use Plugin(Gradient) (on the `background mesh'
view) to generate a vector field. If I save the `background mesh
Gradient' view as a Gmsh msh, it's only got the triangular domain
elements, not the linear boundary elements. If I save the mesh though
(Ctrl-Shift S or File/Save Mesh) it does have the linear boundary
elements.
Anyway, when I apply Plugin(Integrate) to the background mesh Gradient
and then save that as a Gmsh msh, it contains a single point element
at the centre of the domain and the scalar value 0.
1. What does the scalar value 0 mean?
it's the value of the flux of the vector field through the surface (here
the fector field has no z component, hence the flux is zero)
2. How do I get the integrated flux of a vector field through each
Physical Line/Surface boundary patch in two/three dimensions?
you need to generalize the plugin...
Thanks.
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Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine
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