Periodic BC in FV

[wehrad]

Hi everyone,

I'm working on an INSFV app and would need to apply periodic boundary conditions to test it on analytical solutions. I can't seem to find any example of the Periodic Action used in FV, and when I'm trying to add it in [BCs] it's simply being disregarded, (which was somehow expected).

The geometry is a simple 2D block so periodicity should be easy to catch.

Here is my input file: https://github.com/AdrienWehrle/diuca/blob/PR_ViscousFlowFVTests/inputs/viscous_diuca/iceslab_fv_2d_SI_nv.i

I'm on moose-libmesh 2024.12.02 and moose-tools 2024.11.13, and the latest version of moose on master.

Thanks a lot in advance for your help!

[GiudGiud]

Hello

We have only implemented periodic BCs for nodal variables.
For FV, it would be possible to do it through the Functor system:

• create a new object deriving from the FVDirichletBC class
• compute the geometrical transformation from the local face to the face where the value should be the same
• create a functor argument (FaceArg most likely) for that other face
• return the variable_functor(face arg, current state)

This would connect the value on one face to another

[wehrad]

Now trying with periodic velocity on the inclined mesh (with the transform taking the slope of the mesh into account), I still get those near zero velocities with a extremely high viscosity (like 4-5 order of magnitudes above what it should be, which actually makes sense with the extremely low velocities)

[GiudGiud]

and then for FV (on vel_x):

do you have the same kernel for vel_y active?

I think in terms of boundary conditions you should have:

• periodic for vel_x, achieved by setting a dirichletBC on one side equal to the velocity on the other side. (preferably with the BC being upwind, at the higher elevation)
• periodic for vel_y (not sure we need that, but maybe)
• periodic with an offset equal to rho g delta-h between the two sides. That offset is going to be driving the flow, because it's a pressure differential

[wehrad]

do you have the same kernel for vel_y active?

Yes!

• periodic with an offset equal to rho g delta-h between the two sides. That offset is going to be driving the flow, because it's a pressure differential

this makes me think that might be the one I don't have implemented correctly in FV for now, since pretty much no flow is being created. Interestingly, in FE, I don't have this offset either, but flow occurs and in the right way. This might show a difference between FE and FV? Where FV strictly needs this offset while FE generates it by itself?

[wehrad]

this makes me think that might be the one I don't have implemented correctly in FV for now, since pretty much no flow is being created. Interestingly, in FE, I don't have this offset either, but flow occurs and in the right way. This might show a difference between FE and FV? Where FV strictly needs this offset while FE generates it by itself?

However this should be resulting in the inclined mesh case, but even with this inclined mesh, flow is not created. Which makes me even more puzzled.

[GiudGiud]

If you don't have this offset in finite element then something is wrong there. The pressure should not be periodic.

Do you have this boundary condition on top of the new HydrostaticPressure ? This would not be correct

[wehrad]

It seemed like the issue I had with the periodic boundary was some sort of pressure null space, where no flow would be initiated. Now I made the parallel-sided slab very long with regards to thickness (10:1 ratio) and applied the overburden pressure (rhogH*sin(slope)) on both sides, which somehow kicked in flow so it could fully the true gravitational flow with no longitudinal pressure gradient. The slab seems flat here, but slope is applied by projecting gravity.

It gives a ~0.1-0.2% mismatch with the analytical solution on the vertical profile. That's on a very fine mesh though (1.6m resolution in depth for a depth of 100m), and gives quickly higher residuals for lower resolutions. I guess that's because the volume integration requires very high resolution close to the boundaries especially with strong gradients like the base here.

Does that make sense to you @GiudGiud ?

[wehrad]

can you do with an initial condition on velocity instead?

I tried both now while using the periodic BC, but somehow I can't get the gravitational flow to kick off with the periodic BC, only when I set an inlet and outlet pressure with a pseudo infinite slab...

With the periodic BC I still get the same results as some months ago (screenshot of discussion):

[wehrad]

Here is a walkthrough of the steps I did. First, no BC on left nor right, only natural slip BC at the surface and no slip at the bottom. The pressure gives:

Then I set the overburden pressure (rhogh*sin(slope)) at the right boundary:

And then only when I set the same overburden pressure both at the left and right boundary do I see the gravitational flow created without longitudinal pressure gradient:

In that case the slab is not very long so boundary effects are very visible.

Here an example with a much longer slab to make in pseudo infinite:

[GiudGiud]

So in the much longer slab, should you see more of a slope/gradient in pressure like in the shorter case? The gravity / slope is the same right?

A problem with pressure BCs on both sides is well posed as long as there is pressure drop in the system, which you get from the no-slip BC at the bottom.

[wehrad]

So in the much longer slab, should you see more of a slope/gradient in pressure like in the shorter case? The gravity / slope is the same right?

No the gradient in pressure should be the same, since velocity doesn't change along flow and the slope is constant. Which is what I observe, the pressure gradient is the same in both short and long cases.

A problem with pressure BCs on both sides is well posed as long as there is pressure drop in the system, which you get from the no-slip BC at the bottom.

So you mean that pressure BCs on both sides would become an issue the moment there's a free slip at the bottom?

[GiudGiud]

the pressure gradient is the same in both short and long cases.

ok great. It did not like it visually to me.

So you mean that pressure BCs on both sides would become an issue the moment there's a free slip at the bottom?

If you have free slip everywhere and laminar flow you dont have anything to create a pressure drop in the flow. So how would you get the pressure drop from one side to the other?