Finish rotated free-slip prescribed-normal datum: wire FreeSurface consistent solve, pyx API, parallel, nonlinear

[lmoresi]

Context

The rotated strong free-slip constraint now supports a prescribed non-zero wall-normal
datum u.n = ũ_n on the LINEAR solve path (commit 1a08d398 on
feature/free-surface-tangent): one rotated matrix, a switchable datum (0 = free-slip /
held, ũ_n = prescribed radial), differing only in the constraint RHS. Validated serial
in tests/test_1018_rotated_freeslip.py (datum-zero matches free-slip to round-off;
u.n = cos θ imposed to machine precision).

This lets the free-surface consistent solve drop its ill-conditioned penalty natural
BC (penalty=1e5·(n̂·v − ũ_n)·n̂) — the term that trips newtonls line search on an
otherwise linear solve — in favour of the strong rotated constraint.

Remaining work

1. Wire the FreeSurface manager. In free_surface.py::_build_consistent, register
   rotated free-slip on the surface and set consistent._rotated_freeslip_datum = {surface: un_target.sym} (updated each step in _solve_consistent), removing the
   add_natural_bc penalty. Confirm the material-surface advection is unchanged /
   improved (no penalty leak).

2. Clean pyx API. Let add_rotated_freeslip_bc(conds, boundary, normal=...) accept a
   non-zero conds (constant / sympy expr / field .sym) and store it, replacing the
   private solver._rotated_freeslip_datum route. Needs a Cython rebuild. Update
   _classify_walls (currently unpacks 2-tuples) if the stored form changes.

3. Parallel np2/np4. The datum application (_set_rows_local, the xhat ownership
   loop, build_rotation per-node datum eval) is written ownership-safe but untested in
   parallel. Add an np2 case to the datum test.

4. Nonlinear path. solve_rotated_freeslip_nonlinear currently raises on a datum.
   Extend it (the datum enters the constrained residual / initial-feasible guess) if a
   prescribed normal is ever needed with a nonlinear rheology.

5. CBF σ_nn regression. datum=0 is bit-path-identical (so σ_nn recovery is safe), but
   add an explicit test that boundary_normal_traction is unchanged with the new code.

Origin

Found while building a fresh annulus free-surface convection driver and tracing why a
linear solve tripped newtonls (the penalty BC). See also #402 (composition transport
for temperature convection).

Underworld development team with AI support from Claude Code

[lmoresi]

Item 1 done (commit 7134d690 on feature/free-surface-tangent).

FreeSurface._build_consistent now prescribes u.n = ũ_n via the strong rotated
free-slip constraint (add_rotated_freeslip_bc(0, surface, normal=...) +
consistent._rotated_freeslip_datum = {surface: un_target.sym[0]}), dropping the
penalty=1e5 add_natural_bc.

Result: the annulus FS-convection driver runs clean under the default newtonls — 0
DIVERGED_LINE_SEARCH, T in [0,1], vrms/h_max match the old ksponly baseline. The
consistent solve routes through the rotated LINEAR solver (direct KSP), so the penalty's
newtonls line-search thrash is gone; no manual snes_type=ksponly needed. All 16 level_1
free-surface + rotated tests green.

Remaining here: items 2 (pyx datum arg), 3 (np2/np4), 4 (nonlinear path), 5 (CBF
regression test).

[lmoresi]

Item 3 (parallel) done (commit 7c373993). tests/parallel/test_1064_rotated_datum_parallel.py: prescribe u.n = cos θ on the annulus; np1 and np2 give identical datum relL2 (3.98e-5) and ∫v·v matching to iterative round-off — fully partition-independent. The annulus FS-convection driver also runs clean np2 (T in [0,1], results matching serial). Remaining: item 2 (pyx datum arg), 4 (nonlinear path), 5 (CBF regression test).

[lmoresi]

Item 5 (CBF σ_nn regression) — covered by existing tests. test_1018's test_rotated_freeslip_boundary_normal_traction_solcx and test_rotated_freeslip_sigma_nn_lumped_no_overshoot (level_1) pass against the datum code. They exercise the held-solve σ_nn recovery on pure free-slip (datum=0), which takes the bit-identical RHS path, so the traction recovery is provably unchanged.

Status: items 1, 3, 5 done; 2 (pyx datum arg — needs Cython rebuild) and 4 (nonlinear path) remain as focused follow-ups.