Applying wall shear stress to embedded boundary

[QuentinMale]

Hello,

I would like to impose a prescribed wall shear stress on an EB wall (cylindrical surface), while keeping no penetration at the wall.

Concretely, I want:

• No penetration: $\mathbf{u} \cdot \mathbf{n} = 0$
• Specified tangential traction (shear): $\mu \partial u_t/ \partial n = \tau_w$
  For a planar wall aligned with the grid, I would typically enforce this via ghost values in the first off-wall cell. With an EB curved boundary cutting cells, I’m not sure what the recommended approach is in PeleLMeX. Is there an existing mechanism in PeleLMeX to impose a Neumann condition for the tangential velocity components on EB faces (to represent a specified traction), while keeping $u_n=0$?

Thank you very much

[baperry2]

I believe this will be hard to achieve unfortunately. Momentum diffusion in PeleLMeX is implemented implicitly through the AMReX EB LinOp/TensorOp class, which does not appear to support inhomogenous Neumann conditions on the EB: https://amrex-codes.github.io/amrex/docs_html/LinearSolvers.html#embedded-boundaries.

You could perhaps hack something together with the EBInflow capability (see #515), which gets the interior state to set a Dirichlet condition on the exterior, so you could compute what the Dirichlet value needs to be to result in the shear stress you want in the tangential direction while ensuring the normal velocity is 0, but this may not be quite accurate when solving implicitly. It would also be quite cumbersome to handle EB boundaries not aligned with the grid in this manner.

@esclapez and @drummerdoc - any thoughts on how this might be achieved?

[QuentinMale]

Hello Bruce,

Thank you for your answer. I was thinking of a hack that would involve imposing a slip wall, but adding volumetric forcing in the cut cell to impose the wall shear stress. Does that sound like a good idea to you?