Extension of interface-only normal velocity along level-set normals

[Fastaxx]

Description

Hi @maltezfaria 👋

This PR adds support for extending an interface-defined scalar normal speed along level-set normals.

I’m currently working on Stefan-type problems, where the normal velocity ( v_n ) is obtained from an interfacial flux balance and is therefore defined only on Γ. To evolve the level set consistently, a normal extension of ( v_n ) into a narrow band is required (as described for instance in Peng et al., 1999).

What’s added

• extend_along_normals!
  A utility that extends a scalar field away from the interface by solving in pseudo-time:
  $∂_\tau F + \text{sign}(ϕ) n \cdot ∇F = 0, \quad n = ∇ϕ / |∇ϕ|$
  using discretization from Pen et al. 1999

• Optional update hook in NormalMotionTerm
NormalMotionTerm can now take an update callback (similar to AdvectionTerm) so the speed field can be extended at each RK stage.
  Existing usage remains unchanged.

Happy to adapt the API if you prefer a different integration style.

A working prototype is available in my fork:
https://github.com/Fastaxx/LevelSetMethods.jl/tree/feature/extend-velocity-along-normals

Validation and testing

No response

Motivation

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Target audience

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Can you help?

No response

[maltezfaria]

I have needed stuff like this myself in the past, so would be super interested in having this merged! I will take a look at the paper you mentioned. In the meantime, can you please create a PR so that I can more easily compare changes?