[Libmesh-users] Stress-free outflow boundary condition in Navier-Stokes

[David K. <dav...@ba...>]

I'd like to implement the following boundary condition for the outflow 
of a channel:
du/dn - n*p = 0,
where n is the outward normal and p is the pressure. It seems to me that 
this BC would result in an extra boundary term $-\int_{\partial\Omega} n 
p \ds$ being added to the momentum equations?

In my case the outward normal on the outflow boundary is n = (1,0). I 
tried to implement this BC using the following code in side_constraint:

          if (boundary_id == outflow_id)
            Fu(i) -= JxW_side[qp] * p * phi_side[i][qp];

          if (boundary_id != outflow_id)
            Fv(i) += JxW_side[qp] * penalty *
                     (v - v_value) * phi_side[i][qp];

                if (boundary_id != outflow_id)
                  Kuu(i,j) += JxW_side[qp] * penalty *
                              phi_side[i][qp] * phi_side[j][qp];
                if (boundary_id != outflow_id)
                  Kvv(i,j) += JxW_side[qp] * penalty *
                              phi_side[i][qp] * phi_side[j][qp];

where p = side_value(p_var, qp),  plus there are other BCs not shown 
here for inflow and no-slip. This doesn't appear to work; the Newton 
convergence fails with these BCs. If anyone can point out how to 
properly implement this BC, I'd be most appreciative :)

Cheers,
David