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
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