The Fully developed flow boundary condition can be understood from the following figure:
The flow to the domain Ω is assumed to enter through a straight channel of length
L. The channel is a virtual extrusion of the inlet cross section and a pressure constant pressure
Pexit is applied on the inlet of the virtual channel.
The exact value of L is somewhat arbitrary as long as it is not too high or too low.
L is therefore set to ten times the inlet edge length in 2D and to ten times the square root of the inlet area in 2D axisymmetry and in 3D.
where <⋅> denotes the average over the inlet. Since the equation for
Pext is a DAE, it must be solved coupled to Navier–Stokes and it must be treated by a Vanka presmoother and postsmoother if iterative solvers are used.