[Nek5000-users] scalar zero flux bc

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

Hello Neks,

I'm looking for guidance on implementing appropriate volume forcing and zero-net-flux boundary conditions for the scalar equation.

I'm solving

(Eq. 1) phi_t +  U dot grad(phi) = - div(J) + k Laplacian(phi)

where phi is the scalar, phi_t denotes time derivative, and capital letters are vector quantities.  Here, J = J(phi) is modeled flux.

I need zero net flux at the boundaries, which requires

(-J + k grad(phi)) dot N  = 0

or 

(Eq. 2) k grad(phi) dot N = J dot N

where N is the boundary normal.

For (Eq. 1), I am simply using

qvol = -div(J) 

in userq, and I specify the constant diffusivity in uservp (udiff set for ifield.eq.2).  This seems correct, but please let me know if not.

In regard to the boundary condition (Eq. 2), what is the appropriate implementation in userbc and what boundary specification should be used in the .rea file ('c' or 'F')?

Thanks,
Mike