Stratified-ABL Neutral-Limit Regression¶

Status: VALIDATED (neutral-limit regression PASSES on GPU)

Run on GPU (RTX 3060, single precision, all six simulations). The regression passes on both the single block and the 2:1-refined (multiblock) configuration: the feature-inert neutral_limit run reproduces the feature-off baseline to the solver noise floor in both cases. Because the multiblock run matches its baseline to the same floor that the single-block run does, the inert feature composes across the refinement interface (F2C/C2F/border reconstruction) without introducing any discontinuity. See Results. This case makes no physics claim against any external reference - it is a self-regression: the feature-off path IS the reference.

Why this case matters¶

This is the mandatory neutral-limit regression for the stratified-ABL feature - the single most important case in the validation ladder and the one that protects every other developer’s work. A new physical capability (here the Monin-Obukhov stratified IBM ground wall model and the Boussinesq buoyancy coupling) must, with the feature off or at its inert parameter, recover the solver’s pre-feature behaviour exactly. If the feature-off path has moved, the feature has silently changed unrelated physics, and nothing else in the ladder can be trusted until that is fixed.

The stratified-ABL feature’s own development case (examples/mo_stability_validation/mo_stability.nassu.yaml) checks the differential sign of the stability correction (unstable fuller than stable), but there was no committed case asserting that the inert setting is a true no-op. This case fills that gap, on both a single block and, crucially, across a 2:1 refinement interface.

Physical description¶

A minimal half-channel ABL-like box: a flat IBM ground floor (EqLog wall model) at \(z = 1\) in a \(64 \times 32 \times 64\) domain, periodic in \(x\) (streamwise) and \(y\) (spanwise), no-slip at the bottom, free-slip at the top. A streamwise body force \(F_x\) drives the flow against the wall drag, LES Smagorinsky is on, and one coupling scalar temperature rides the shared DDF scalar path (advected and diffused, with a mild vertical gradient from a warm floor). All quantities are in lattice units; the setup is modelled directly on the stratified-ABL development case so the regression exercises the identical code path.

The regression pair¶

Two simulations that must produce statistically identical results:

Simulation	`mo_stability`	Buoyancy	Meaning
`baseline`	absent	`beta = 0`	pre-feature neutral path (feature OFF)
`neutral_limit`	`surface_heat_flux = 0`	`beta = 0`	feature code path ACTIVE but inert

In baseline the feature is entirely off: no mo_stability block, and the buoyancy is inert - \(f_\mathrm{buoy} = -\rho_0\,\beta\,(\phi - \phi_\mathrm{ref})\,g\) is exactly zero because \(\beta = 0\). The wall model is the plain EqLog log law; temperature is a passive tracer.
In neutral_limit the feature is present but at its inert parameter: mo_stability with surface_heat_flux = 0 drives the Obukhov length \(L \to \infty\), so \(\zeta = z/L \to 0\) and the momentum stability function \(\psi_m = 0\) - the neutral log law (the schema documents surface_heat_flux = 0 as “recovers the neutral log law”). Buoyancy stays inert (\(\beta = 0\)). The mo_stability code path executes but must reproduce baseline.

Multiblock variant¶

The same pair (baseline_mb, neutral_limit_mb) is run across a 2:1 refinement slab: a full \(x\)-\(y\) band at \(z \in [16, 32]\). This puts two \(z\)-normal coarse-fine interfaces directly in the path of the vertical temperature gradient, so the regression exercises F2C (fine->coarse), C2F (coarse->fine spatial + temporal interpolation) and the same-level border population reconstruction / init-borders path. This is the highest-value composition rung: it is exactly where Nassu’s most damaging bugs have lived (a term correct in bulk collision but omitted from border reconstruction or the level-transfer rescale - e.g. the porous Darcy-force sawtooth, the forked-scalar C2F bug). The inert buoyancy force and the temperature field must stay continuous across the interface, with no per-block sawtooth.

Validation ladder and composition matrix¶

This case fills the entire neutral-limit-regression row of the stratified-ABL feature’s composition matrix. LES, the temperature scalar and the IBM ground wall model are all present simultaneously in both the single-block and the multiblock cells, so every applicable cell of the row is covered by this one case:

                    | single-block | multiblock | +LES | +scalar | +IBM
neutral limit (07)  |     reg      |    reg     |  reg |   reg   |  reg

reg = neutral-limit regression, covered here (feature-off / inert recovers the pre-feature path to the solver noise floor). The X benchmark rungs of the ladder (canonical stratified references + acceptance criteria) live in the sibling cases 05 (vc_stratified_street_canyon) and 06 (vc_stratified_building); this case is the regression foundation they rest on.

Numerical acceptance criterion¶

The GPU solver is not bit-reproducible run-to-run (atomicAdd ordering, ~\(10^{-6}\) relative in float32), so the regression validates statistics, not instantaneous fields, and proves parity the robust way - by comparing against the solver’s own noise floor. Concretely, using the time-averaged (mean) profiles over \([10000, 20000]\) steps, \(x\)-\(y\)-averaged into \(z\)-profiles of \(u(z)\), \(\rho(z)\) and \(\mathrm{temperature}(z)\):

\[\Delta_\mathrm{feature} = \big\| \overline{q}_{\,\mathrm{neutral\_limit}}(z) - \overline{q}_{\,\mathrm{baseline}}(z) \big\| \;\; \lesssim \;\; \Delta_\mathrm{noise} = \big\| \overline{q}_{\,\mathrm{baseline\_rerun}}(z) - \overline{q}_{\,\mathrm{baseline}}(z) \big\| \qquad (\sim 10^{-6}\ \text{relative}),\]

for each profiled quantity \(q \in \{u, \rho, \mathrm{temperature}\}\). That is: the neutral_limit-vs-baseline difference must be the same order as a baseline-vs-baseline rerun difference (pure solver noise). The baseline_rerun / baseline_mb_rerun simulations exist solely to establish that noise floor within a single nassu run invocation.

For the multiblock variant, additionally require the temperature (and hence the inert buoyancy) field to be continuous across the \(z = 16\) and \(z = 32\) refinement interfaces to the same noise floor - no per-block sawtooth or jump in the mean field straddling the interface.

The regression fails if \(\Delta_\mathrm{feature} \gg \Delta_\mathrm{noise}\) for any profiled quantity, or if a sawtooth appears at the multiblock interface: either means the (supposedly inert) feature code path has perturbed the pre-feature physics and must be fixed before any benchmark rung is trusted.

Simulation setup¶

All values are in lattice units (modelled on the stratified-ABL development case). Single-block level-0 grid; the multiblock variants add one refinement level over the mid slab.

Parameter	Value (lattice)
Domain \((x, y, z)\)	\(64 \times 32 \times 64\), `block_size` 8
Periodicity	\(x\), \(y\) periodic; \(z\) walls (B / F)
Bottom / top BC	RegularizedHWBB (no-slip) / RegularizedNeumannSlip (free-slip)
Driving force \(F_x\)	\(1.7\times10^{-6}\)
Relaxation time \(\tau\)	0.51 (\(\nu = 3.33\times10^{-3}\), \(\mathrm{Ma}\) well below 0.1)
Fluid velocity set / operator	D3Q19 / RRBGK
LES model	Smagorinsky \(C_S = 0.17\)
Ground wall model	IBM EqLog (\(z_0 = 0.1\), `dist_ref` 5, `dist_shell` 1.5)
Coupling scalar	`temperature` (D3Q7 / RRBGK, \(D = 5\times10^{-3}\))
Buoyancy	INERT (\(\beta = 0 \Rightarrow f_\mathrm{buoy} = 0\))
MO stability (neutral_limit)	`surface_heat_flux = 0` (\(\Rightarrow\) neutral log law)
Multiblock refinement	full \(x\)-\(y\) slab at \(z \in [16, 32]\), level 1 (2:1)
Steps / stats window	20000 / \([10000, 20000]\) (P5-tunable)

There is no external reference dataset; the baseline run is the reference (see reference/README.md).

Results¶

The comparison notebook (07_stratified_neutral_limit.ipynb) is executed against the GPU run and presents results as PLOTS (overlaid neutral_limit-vs-baseline profiles and a parity bar chart against the solver noise floor), never a bare table. Measured relative-L2 profile differences:

Quantity	Single block \(\Delta_\mathrm{noise}\) / \(\Delta_\mathrm{feature}\)	Multiblock \(\Delta_\mathrm{noise}\) / \(\Delta_\mathrm{feature}\)
\(u\)	\(5.5\times10^{-7}\) / \(3.4\times10^{-7}\)	\(1.1\times10^{-6}\) / \(8.5\times10^{-7}\)
\(\rho\)	\(3.0\times10^{-8}\) / \(1.5\times10^{-8}\)	\(2.6\times10^{-8}\) / \(1.5\times10^{-8}\)
temperature	\(6.0\times10^{-7}\) / \(3.0\times10^{-7}\)	\(1.8\times10^{-7}\) / \(1.8\times10^{-7}\)

For every quantity, in both topologies, \(\Delta_\mathrm{feature} \leq \Delta_\mathrm{noise}\) - the feature-inert path differs from baseline by no more than a baseline-vs-baseline rerun does, i.e. by pure solver noise. The multiblock pair sits at the same floor as the single-block pair, so the refinement interface (F2C/C2F/border reconstruction) introduces no feature-induced discontinuity. The neutral-limit gate is met. (Table shown beneath its plots in the notebook, per the plots-not-tables convention.)