"Do Nothing" Inflow Condition in NS Tutorial

Question

Hi all,

In demo #6, the incompressible Navier Stokes equations, found at

https://fenicsproject.org/documentation/dolfin/1.0.1/python/demo/pde/navier-stokes/python/documentation.html

the authors "impose free flow ('do nothing') boundary conditions for the velocity and no-slip boundary conditions on the remaining boundary."

I understand that the flow is driven by a time dependent pressure term at the inflow. I also understand the "do nothing" outflow condition is rather common in CFD. What I do not understand is how one can get away with prescribing "do nothing" at the inflow. Of course the demo runs just fine, but it seems both unphysical and mathematically ill posed to not prescribe an inflow condition.

Can someone please help shed light on what is going on here?
Best,
-Sean

Answer 1

The flow is driven by pressure, just as in physical reality, we don't need to specify flow rates, only inlet and outlet pressure.

Answer 2

As Chris says, there is nothing unphysical about assigning a pressure drop
through the domain. This is what you would you typically would do in an physical
experiment, right? Sometimes numerical instabilities do however occur
because the convection-diffusion equation for the velocity is no longer coercive.