Inviscid flow an free slip BC

[Eilloo]

Hello all,

I am trying to run inviscid flow simulations, to later use as an initial condition for the viscous case in the FE INS module.

However, I have not found a way to implement a free slip/no penetration boundary condition for my geometry - in this case, an aerofoil.

I had thought that a Neumann BC of zero for all velocity components at the boundary would do the trick, and attempted to implement this using 'ADVectorFunctionBC'.
However, the solution for this was the same as my initial condition (constant velocity for the whole domain), with the flow not moving around the obstacle. The outlet boundary condition was constant pressure = 0.

I came across this thread when looking for a solution: #21418
However, I am having trouble understanding the difference between the 'no flux' and 'no penetration' cases described here, as well where the mentioned approaches are implemented (ie - can this be done through a moose input file, or would custom BCs be required?)

My question then, is: Have I misunderstood the relationship between Neumann BCs and the no penetration condition, and what is the proper way to implement the free slip condition for inviscid flows in FE, rather than FV?

Thanks!

[GiudGiud]

Hello

Are the flow variables defined inside the aerofoil as well?
In other words, is the aerofoil boundary inside the flow domain or well on the boundary?

Which variable set are you using (velocities or momentum?) ? For whether we have it or not

Guillaume

[lindsayad]

Hi @doquang it's a good question. The natural condition on the walls for the mass equation do implicitly accomplish the zero normal velocity condition. INSFEFluidWallMomentumBC is perfectly valid to add as it allows for non-zero normal stresses. If you did not impose that BC, then you would be imposing these additional conditions at the walls through the natural condition:

$p \vec{n} - \mu \nabla \vec{v} \cdot \vec{n} = \vec{0}$

Now I don't know what the purpose of INSFVMomentumFreeSlipBC is in this case. I commented out that boundary condition and ran the simulation and to me the results look good. Maybe @lingzou could weigh in on this

[lingzou]

For this case, with or without the INSFVMomentumFreeSlipBC look almost the same. In some cases I have seen before, WITHOUT the free slip BC, velocity on a wall would NOT aligned with the wall perfectly so I used that BC to 'help' align the velocity with wall. (unfortunately I now cannot find that case but it did exist 🙄).

If in your case, the velocity alignment is good (or acceptable), I'd suggest just to ignore the INSFVMomentumFreeSlipBC.

[doquang]

Thanks @lingzou and @lindsayad. BTW, do you have any documentation to learn about how INSFE is implemented. For example, why does INSFEFluidMassKernel add the advective term of mass conservation equation along with pressure-stabilized Petrov-Galerkin terms. I mean masseq_part. Is this not the same as the implementation in the INS and INSAD modules, right?

[lingzou]

Section 9 of SAM theory manual (https://publications.anl.gov/anlpubs/2021/05/166771.pdf), or more specifically, equation (9.29), should answer your question.

[sorry that the codes have been merged but the documentation part we haven't finished.]

[lindsayad]

It is the same apart from the fact that for INSMass and for INSADMass we do not integrate the $\psi \nabla \cdot \vec{v}$ term by parts. You must include $\psi \nabla \cdot \vec{v}$, whether integrated by parts or not, because that is the physics, it is the math enforcing conservation of mass. PSPG is just a stabilization term you add on top of it