Add the Brinkman kernel

[alexfikl]

This adds the Brinkman kernel and the corresponding Brinkman stress tensor. I'm not particularly sure the scaling is right (the 2-3 papers I've found all had different scaling), but I've checked (in Mathematica) that

• The kernel itself (with the pressure kernel) satisfies the Brinkman equation.
• The stress matches $-p_j \delta_{ik} + \mu (\partial_i K_{jk} + \partial_k K_{ij})$.
• The limits as $k \to 0$ gives back the Stokeslet and Stresslet with the scalings that we already have.

Also added these to some tests: test_pde_check_kernels and test_translations. There's probably more things we could test, but it should be ok for now.

TODO:

• There's also a stress tensor for this (matching the Stresslet).

[Copilot]

Pull request overview

Adds support for a Brinkman (Brinkmanlet) kernel to sumpy.kernel, together with test coverage to exercise PDE checks, translations, and pickling.

Changes:

• Introduce BrinkmanletKernel as an ExpressionKernel with loopy/codegen support for special functions (2D Hankel form).
• Extend kernel PDE-check tests (test_misc.py) to include Brinkmanlet components in 2D/3D.
• Extend kernel translation/pickling tests (test_kernels.py) to include Brinkmanlet and its runtime parameters.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

File	Description
sumpy/kernel.py	Adds BrinkmanletKernel, mapper hookups, and updates a comment in YukawaKernel.is_complex_valued.
sumpy/test/test_misc.py	Adds PDE-check parametrization coverage for BrinkmanletKernel in 2D/3D.
sumpy/test/test_kernels.py	Adds translation and pickle test coverage for BrinkmanletKernel, including runtime args (mu, k) and custom arg names.

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[alexfikl]

Does this a * delta_ij get flattened somewhere? Is it better to flatten it here?

[Copilot]

Pull request overview

Copilot reviewed 4 out of 4 changed files in this pull request and generated 4 comments.

[alexfikl]

For what it's worth, doing the test_translations tests for these Brinkman things is quite slow compared to the other kernels in there 😁