Pressure-induced flow

Hello
I'm struggling with setting up a 2D CFD (Navier Stokes) Simulation where the flow is induced by a pressure difference.
Let's assume we're having a perfect 2D pipe and we want to apply a certain pressure at one boundary surface and the other surface to be at ambient pressure.

Independent of material properties (I tried it with air and water) and of the applied pressures, the solution will not converge. I even run a simulation with an inflow velocity as BC, then computed the pressure, and in a second simulation, I took exactly this pressure as BC. It still didn't converge...

Thanks for any help
Leon

Although it intuitively should work to set-up a pressure drop problem by just prescribing differing pressures, the finite element method also implicitly prescribes homogeneous Neumann (flux) boundary conditions on non-Dirichlet (fixed value) boundaries. In the case of prescribed pressure boundaries this means that the momentum equations will also have an implicit condition like "(-p*I + ux_i)*n = 0" affecting the pressure, which must be negated to get the expected solution. Alternatively one can prescribe periodic boundaries with a given pressure drop.

Unfortunately, both these approaches require some non-standard modifications of the fea data struct which currently can not be done in the FEATool GUI. However, there is an m-file script model example showing how to do this on the MATLAB command line (the full code listing can be found in the examples/ex_navierstokes14.m subdirectory of the FEATool installation directory):


MATLAB m-file script example for flow in a channel driven by a pressure difference

Leon Robers wrote

I'm struggling with setting up a 2D CFD (Navier Stokes) Simulation where the flow is induced by a pressure difference.
Let's assume we're having a perfect 2D pipe and we want to apply a certain pressure at one boundary surface and the other surface to be at ambient pressure.

Independent of material properties (I tried it with air and water) and of the applied pressures, the solution will not converge. I even run a simulation with an inflow velocity as BC, then computed the pressure, and in a second simulation, I took exactly this pressure as BC. It still didn't converge...

Alright, thanks for the quick reply!
Am I right in the assumption that this will also work in 3D and with more complex geometry? (after changing the code accordingly)

Yes, 3D should work similarly.

Leon Robers wrote

Am I right in the assumption that this will also work in 3D and with more complex geometry? (after changing the code accordingly)

So the example "ex_navierstokes14" was a good starting point to apply pressure BC to my slightly more complex model. But I needed to change the shape function for the pressure from first order to second order so that the simulation converged (Just as a hint for someone who wants to do something similar)

Best,
Leon