Normal Stress Boundary Condition
The total stress on the boundary is set equal to a stress vector of magnitude f0, oriented in the negative normal direction:
using the compressible/weakly compressible and the incompressible formulation, respectively.
This implies that the total stress in the tangential direction is zero. This boundary condition implicitly sets a constraint on the pressure which for 2D flows is
(3-30)
If un/∂n is small, Equation 3-30 states that p ≈ f0.
The Normal Stress condition is the mathematically correct version of the Pressure Conditions condition (Ref. 4), but it is numerically less stable.