CFD Online Discussion Forums - Incompressible pressure boundary condition on a wall

Hello all,

the "standard" OpenFoam incompressible boundary condition on a wall seems to be $\frac{\partial p}{\partial n} = 0$ , however if you take the normal derivative of the NS-equations you end up with:
$\frac{\partial p}{\partial n} = \nu \Delta u_n - \frac{\partial u_n}{\partial t} + \vec u \cdot \nabla u_n.$
Let us assume that the velocity (both tangential and normal) on the boundary is zero. Then the last two terms vanish and the pressure gradient in normal direction (on the boundary) reduces to:
$\frac{\partial p}{\partial n} = \nu \frac{\partial^2 u_n}{\partial n^2}.$
I think this terms vanishes like $\frac{1}{Re}$ - but still why is this term neglected in the "standard" incompressible boundary condition? Numerical reasons?

Best regards
Moritz