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

(13-14)

If ∂un/∂n is small, Equation 13-14 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.