Maxwell-accommodating wall boundary conditions (opt-in :wall face)

[sbryngelson]

Adds grid-aligned kinetic walls — the capability gap that blocked microflows entirely (slip, temperature jump and the Knudsen layer are the physics there) and also blocked Couette/Fourier validation. Opt-in; defaults unchanged, no golden moves.

Physics

A wall is a half-space moment problem, and a 35-moment vector cannot encode the split. The ghost form is therefore an approximation — but two of its three ingredients are exact:

M_ghost = alpha * M_Maxwellian(rho_w, u_w, T_w) + (1-alpha) * M_specular(M_int)

• specular (alpha=0) is EXACT — reflection maps v_n -> -v_n, i.e. M_{ijk} -> (-1)^i M_{ijk}, a sign flip on moments of odd normal order. Measure-preserving, so realizable in, realizable out, with tangential velocity untouched (free slip).
• diffuse (alpha=1) sets rho_w from zero net normal mass flux, the incoming flux being a closed-form half-space Gaussian integral. This Gaussian assumption is the one real approximation.
• the blend is convex, so realizability follows from the same argument bgk_relax_tup and theta*-IDP already rest on — no projection, no new failure mode.

Halo-refill only: no changes to the residual, WENO5, theta-IDP or the flux kernels*, so it works at every spatial order and on GPU immediately.

Ghost layer k mirrors interior layer k rather than copying the nearest cell — specular reflection of a half-space is the mirror map, which is load-bearing at order 3 (g=8). On GPU this is why _axis_src returns a mirrored index plus a wall_side flag: unlike :inlet, whose ghost is a constant vector, a wall ghost is a function of the adjacent interior cell.

The slip coefficient — measured, and it works

The design deliberately left open whether the Gaussian half-space assumption reproduces Maxwell slip. It does:

alpha	zeta measured	(2-alpha)/alpha	implied sigma_p
1.00	1.1853	1.000	1.185
0.75	1.7209	1.667	1.033
0.50	2.8435	3.000	0.948

The (2-alpha)/alpha accommodation scaling is reproduced, and sigma_p = 0.95–1.19 against a theoretical 1.0–1.1. Interior profiles linear to R^2 = 0.99999.

So no escalation is needed. Had this been badly off, the fix would have been a prescribed wall flux (KFVS-at-wall), touching the residual and the theta*-IDP anchor. It isn't.

lambda uses the shared convention lambda_mu = mu/(rho sqrt(2RT)) = tau_ref*sqrt(Theta/2) — the same one bridged to SPARTA, so the number is comparable across codes.

Verification

• equilibrium wall is an EXACT fixed point — max|dM|/|M| = 0.000e+00 on both CPU and GPU, bitwise. This is the test that catches a wrong rho_w normalization: a factor error in the half-space mass balance shows up here and nowhere else, so exactly zero says the balance closes analytically.
• specular: mass drift 0, energy drift 0, tangential velocity preserved at exactly 0.300, with T_w = 99 set absurdly to prove it is ignored.
• half-space influx closed form vs numerical quadrature: 3.3e-7 (independent computation).
• unit gates W1–W5: 265/265, registered in runtests.jl.
• full suite 1689 passed / 5 broken / 0 failed / 0 errored = 1424 baseline + 265 new; stdout diffed against baseline is identical apart from the new tests' own output.

Also fixed — all found while finishing this

• Walls were unreachable by users. simulation_runner never populated WALL_SPEC, so the feature only worked if a caller poked the global directly, as the tests did. Now wired via a wall_spec param, with a warning if a :wall face is set without one. Verified end-to-end through the runner.
• test_wall_bc.jl was not in runtests.jl — CI would not have run it.
• HIGHORDER.md was a generation stale — the doc handed to Fox and Posey. It called itself notes on the projection35-port branch, listed spatial_order as only 1 or 2, and said the scheme was "not yet robust at Ma=100". Order-3 has been the default since High-order WENO5 + θ*-IDP (CPU+GPU, DRY) — order-3 as default #18 and Ma=100 is CI-guarded. Refreshed with dated correction notes, keeping the Ma=100 failure-mechanism paragraph (the cancellation in u = M100/M000 at rho~1e-5 is still what to understand when a high-Ma run misbehaves). Also added an options table it lacked entirely — Pr, omega, stage_bgk_exact and :wall/wall_spec were documented nowhere a collaborator would look, so someone could match omega to argon, get Pr right, and still have mu 1.85x low with no warning.

Scope / not done

Grid-aligned faces, stationary in the normal direction (tangential motion allowed — covers Couette, Fourier, planar microchannel). Immersed and curved walls are a separate spec — that is what would fix the cylinder case's held-gas bounce-back and its ~10% blockage.