[Nek5000-users] Mixed boundary condition for fluid velocity

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

Dear Nek users and developers,

I am working on turbulent flow over porous walls. Instead of no slip condition for rigid walls, I need to implement the following boundary condition for the fluid velocity on the porous walls

u = c1 Sigma . N + F(Sigma)

where,
c1 — a scalar constant
u — fluid velocity
Sigma — fluid stresse tensor
N — Normal vector
F(Sigma) — a simple linear function of fluid stresses.

If F(Sigma)=0, then the implementation is straightforward (similar the convection boundary condition implementation for heat transfer problem).  It is not clear to me how to incorporate F(Sigma). Could someone explain me how can I add an unknown term (involving surface integration) into the boundary conditions? I have already looked into the code but could not understand where the surface integral coming out of the integration by parts (in the stress formulation) is added to the system matrix in the code. Could someone also point me out where this is done?

Thank you very much,

Best regards,
Sudhakar 
KTH-Mechanics.