Nodal value of an unknown in weak formulation

1

Hi,

I have an 1D problem of Navier-Stokes on a domain from r = 0 (symmetry) to r = 1 (no-slip). After integration by parts of the viscous term, the values of the shear stress (trz) at r=0 and r=1 are presented in the weak formulation. I dont want to delete them from the weak form. The question is how we introduce such terms (nodal values of the unknown) weakly?

This is the weak form of the momentum in cylindrical coordinates. v is velocity and trz is shear stress. The driven force is the axial pressure gradient and the equation is written in normalized form.

Res  = ( Re*(1./dt)*(v-v0)*phi[0] - phi[0] - (1./x[0])*trz*phi[0] + trz*phi[0].dx(0) ) * dx

So I want to add two extra terms on the previous equation. trz on r = 0 and trz on r = 1.

Thanks

2

Why do you want to introduce these terms?

The symmetry boundary condition is dv/dr=0, which gives \tau_{rz}=0 at the symmetry boundary and thus this boundary term disappears.

On the the zero-slip boundary, the test function \phi is 0 by definition, so this term will also disappear.

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