Hi,

I am working on a 3D Control Volume based FEM code that uses an unstructured tetrahedral mesh. Unknowns are located at the mesh vertices. Now I came upon the following problem, setting the values at a boundary:

Consider a simple channel with 1 inlet, 4 walls and 1 outlet. At the inlet, v=(1,0,0). Now the vertices at the edges that form the inlet belong to two different boundary faces. Each of them to a wall _and_ to an inlet. Which is now the correct velocity value to set at these vertices? The ones from the inlet (v=(1,0,0)) or the ones from the wall (v=(0,0,0))?

Regards, Matthias

Matthias,

The correct BC for any node that is on a wall is a wall (non-slip) BC. The way many codes handle BC assignement is to set the wall BCs last. That way any node on a wall (even if it is at a junction of a wall and something else) gets a wall BC.

Regards, Alton

You will run into all kinds of difficulties like this trying to set boundary conditions directly on a vertex. Set boundary values on boundary faces and when you discretise the control volume boundary flux use the set value.

On the inlet it will be the specified velocity, and on the wall the velocity is zero. This is unambiguous.

Dan.

Yes, I agree that I have to set the boundary values on the boundary faces and I also use this value to compute the boundary flux. But what do I do with the other control volume faces? I use Gauss quadrature to do the integration on the other control volume faces and I need the values at the CV vertices to do so. So what do I do here?

Matthias.

At the inlet edges, the right b.c. will be v=(1,0,0). Where as at the exit edges, it will be v=(0,0,0). At the inlet if you are interested in uniform velocity profile, you have to specify v(1,0,0) otherwise there will be a deficit in the mass. But if you are specifying a profile, e.g. a parabolic, v=(0,0,0) will have to be specified. Hope, it may help.

GS

A boundary vertex value is "solved for", just like any other interior vertex value. You only use the boundary condition to close the flux through the boundary face.

If you are running implicit you end up with coefficients (from your gauss quadrature) which multiply that vertex value at the next (implicit) time level.

If you are running explicit you just multiply out the coefficients times the previous (solved for) value. The "solved for" values simply satisfy conservation for the control volume on the edge between the wall and the inlet. On the first timestep the vertex value will just be your initial guess.

Dan.

Thanks! That's a good hint. I will give it a try!

Matthias