Anchored Dual-pass HLLD for Hypoelasticity (+ HLLC and interface-consistent HLL)

[ChrisZYJ]

Description

Adds:

1. Hypoelasticity: Anchored Dual-pass HLLD
2. Hypoelasticity: HLLC
3. Hypoelasticity: HLL option (interface-consistent)
4. HLL option (alpha div U) so non-conservative treatment aligns with HLLC

Key Design Choices

Separate HLLD Riemann Solvers

At a glance it might be tempting to combine HLLD MHD with dual-pass hypoelasticity HLLD, but keeping them separate makes the code cleaner and much easier to maintain because:

1. Unlike HLL or HLLC, HLLD is a class of HLLD-type solvers, with formulas and states dependent on the eigenstructure of the governing equations, so the inner states' equations are completely different for MHD vs Hypoelasticity.
2. HLLD hypoelasticity has a newly developed dual-pass anchored form, making it different from any convenional HLLD Riemann solver. The anchored forms are necessary for the non-conservative hypoelasticity terms, which MHD does not have.
3. MHD and Hypoelasticity deal with completely different physical regimes with different governing equations, and any changes or new physical models added in the future will not apply to both modules at once.

Riemann Source Terms

For the non-conservative terms, unlike the usual governing equations that only need div U i.e. du/dx, dv/dy, dw/dz (alpha div U, K div U, etc.), Hypoelasticity has cross terms like du/dy, so we must also pass those Riemann-consistent traces from Riemann solver to the rhs. (The old Hypoelasticity code with the HLL Riemann solver uses finite difference for non-conservative rhs, which provides enough stability given that HLL smears the interface immediately, so there wasn't a need to pass the du/dy traces before this PR. But that does not work for HLLC/HLLD for Hypoelasticity.)

Also grouped/named the condition branches (with lots of comments within the code):

Branch	Face quantity read	RHS formula per $\alpha_k$	K*div(u) velocity source
adv_src_alpha_iface	flux_src_n(dir)%vf(j_adv) = per-fluid $\Psi_{\alpha_k}$	$u_\text{cell} \cdot \Delta\Psi_\alpha / \Delta x$	nc_iface_vel_n(dir)%vf(1)
adv_src_vel_iface	flux_src_n(dir)%vf(adv\%beg) = shared $\Psi_u$	$\alpha_k \cdot \Delta\Psi_u / \Delta x$	Same flux_src_n slot (already $\Psi_u$)
adv_src_none	—	Skipped (HLLD handles internally)	—

The derivations, meanings, and usage of the Riemann source variables are not straightforward. I've added some hopefully very helpful notes in misc/dev_notes for future developers (or AI agents; directing them to my notes should help them make fewer mistakes with the source terms) in terms of the understanding and derivations for the HLL/HLLC non-conservative fluxes, and their variable mapping for Riemann solvers and RHS.

Backwards Compatibiilty

• All default behaviors preserved exactly (newly added features as options)
  • The only exception is the removal of an incorrect ad-hoc fluids-limit guard that affects only Hypoelasticity HLL
• All existing usage of Riemann and rhs source terms are preserved. No refactor is done to keep the scope of this PR limited (any refactoring would touch most of the existing HLLC functionalities)

Type of change

• New feature

Testing

• All tests passed locally on CPU and Nvidia GPU, and on Frontier.

• Smooth Eigenmode Convergence

• Weak Solution Comparison (Rodriguez & Johnsen (2019) §5.3(b))

• Weak Scaling on Frontier

Checklist

• I added or updated tests for new behavior
• I updated documentation if user-facing behavior changed
• GPU results match CPU results
• Tested on NVIDIA GPU or AMD GPU

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[sbryngelson]

very impressive! but we're definitely going to need a Riemann solve refactor before merging this. it's all just too cumbersome.