(vc_stratified_building)= # Stratified Isolated Building (Zhou et al. 2021) ```{admonition} Status: RUNS at full resolution (finite through the early transient) - NOT yet a benchmark match --- class: warning --- The full stratified-ABL stack in this case COMPILES, BUILDS and RUNS on GPU at the committed full resolution (320x240x200 domain, building refined to level 2): it fits comfortably (~6.5 GB allocated on a 12 GB GPU) and integrates the SEM velocity inlet, the buoyant `temperature` scalar, the flux-driven Monin-Obukhov IBM ground wall model, the z-varying scalar inlet, the voxelized building and the passive pollutant ground source together, staying finite through the early transient (past step 1000, ~420 MLUPS; no NaN/inf in `rho`, `u`, `temperature_phi` or `pollutant_phi`). No physics agreement is claimed: the reference-data digitization, provisional-parameter tuning and a statistically-converged run remain for phase 5 (epic #1034, issue #1039). (The sibling canyon case 05, by contrast, diverges early at full resolution and needs its provisional parameters stabilised first.) ``` ## Why this case matters An isolated building in an unstable boundary layer is the canonical bluff-body dispersion problem with buoyancy: the recirculation behind the building shrinks as instability grows, and the near-source concentration responds directly. It complements the street-canyon case with an isolated obstacle and, crucially, a graded Richardson-number ladder that tests the stratified stack across a range of stabilities rather than at a single point. The reference is the large-eddy simulation of {footcite:t}`zhou2021large`, validated against the Tokyo Polytechnic University (TPU) Database 2006 wind tunnel for the two least-unstable cases. ## Physical description A single rectangular building (footprint $0.5H \times 0.5H$, height $H$, so a height-to-width ratio of 2:1) sits in an unstable atmospheric boundary layer. A hot ground under cooler inflow air sets the instability. A ground-level hole source 0.25$H$ behind the leeward wall releases a 5% ethylene / 95% air mix, a near-neutral-density tracer treated as a passive scalar. In nassu the building is voxelized (velocity no-slip, adiabatic and impermeable scalar walls), the buoyant temperature is an active Boussinesq scalar, and the ground uses the Monin-Obukhov stratified wall model coupled to that temperature. The approach flow is the Synthetic Eddy Method (SEM), the nassu analogue of Zhou's Vortex Method, with a z-varying MEAN temperature inlet (no temperature fluctuation, matching the paper). ```{admonition} Modelling mismatch (state when comparing) --- class: note --- Zhou et al. solve the incompressible-ideal-gas energy equation (variable density, buoyancy $\rho g$). Nassu reproduces the cases with the BOUSSINESQ surrogate (constant-density base state, linear buoyancy force). The tracer is near-neutral-density ethylene, so the passive-scalar pollutant is defensible. A near-source discrepancy at the strongest instability ($\mathrm{Ri} = -1.5$) may reflect the dropped density variation and must be stated explicitly at P5. ``` ## Stratification specification (Zhou's Richardson number) Zhou et al. define the bulk Richardson number (their Eq. 1) as ```{math} \mathrm{Ri} = \frac{(g / T_r)\,(T_r - T_g) / H}{(u_H / H)^2}, ``` with $T_g$ the ground temperature and $T_r$ the inflow temperature at building top. The six cases span $\mathrm{Ri} = 0, -0.1, -0.3, -0.6, -1.0, -1.5$. In nassu the buoyancy is sized from this Ri with a normalized temperature ($\phi = (T - T_r) / \Delta T$, $\Delta\phi = 1$ ground-to-reference): $\beta g_\mathrm{lat} = |\mathrm{Ri}|\, u_{H,\mathrm{lat}}^2 / H_\mathrm{lat}$. This scaffold builds **Case 2** ($\mathrm{Ri} = -0.1$). ### Richardson-number ladder Only Case 1 ($\mathrm{Ri} = 0$) and Case 2 ($\mathrm{Ri} = -0.1$) are wind-tunnel-backed (TPU Database 2006); Cases 3-6 are CFD-only and their comparison is Zhou's own LES, not measurements. The lattice velocity is fixed at $u_{H,\mathrm{lat}} = 0.05$ for all cases, so only $\nu$ (from Re) and the buoyancy $g_\mathrm{lat}$ (from Ri) change: | Case | Ri | Re | $u_H$ (m/s) | $\tau$ | $g_\mathrm{lat}$ | Backing | | ---- | ------ | ----- | ----------- | --------- | ----------------------- | ----------- | | C1 | 0.0 | 14811 | 1.37 | 0.5003241 | 0.0 | wind tunnel | | C2 | $-0.1$ | 14811 | 1.37 | 0.5003241 | $7.8125\times10^{-6}$ | wind tunnel | | C3 | $-0.3$ | 8545 | 0.79 | 0.5005617 | $2.3438\times10^{-5}$ | CFD-only | | C4 | $-0.6$ | 7572 | 0.70 | 0.5006340 | $4.6875\times10^{-5}$ | CFD-only | | C5 | $-1.0$ | 7031 | 0.65 | 0.5006828 | $7.8125\times10^{-5}$ | CFD-only | | C6 | $-1.5$ | 7031 | 0.65 | 0.5006828 | $1.171875\times10^{-4}$ | CFD-only | The case YAML sketches an `!unroll` template (bottom of the file) that P5 can activate to run the whole ladder; the per-case $\tau$ and buoyancy are taken from this table. ## Pollutant source A ground **hole source** (diameter 5 mm) centred 0.25$H$ behind the leeward wall, emitting a 5% ethylene mix at $q = 2.62 \times 10^{-4}\, u_H H^2$ (constant across cases). Results are the dimensionless concentration $\langle c \rangle / c_0$ with $c_0 = 0.05\, q / (u_H H^2)$ (the 0.05 is the tracer fraction). ## Simulation setup (Case 2) | Parameter | Physical | Lattice (level 0) | | --------------------------------------- | ----------------------------- | -------------------------------------------- | | Building height $H$ | 0.16 m | 32 cells | | Building footprint | $0.5H \times 0.5H$ | $16 \times 16$ cells | | Reference velocity $u_H$ | 1.37 m/s | 0.05 ($\mathrm{Ma} = 0.087$) | | Reynolds number | 14811 | 14811 | | Relaxation time $\tau$ | - | 0.5003241 ($\nu = 1.080\times10^{-4}$) | | Richardson number | $-0.1$ | $\beta g_\mathrm{lat} = 7.8125\times10^{-6}$ | | Temperature difference | $\Delta T = 34$ K | $\phi \in [0, 1]$ (normalized) | | Prandtl / Schmidt | $\mathrm{Pr}=\mathrm{Sc}=0.7$ | $D = \nu / 0.7 = 1.543\times10^{-4}$ | | Turbulent $\mathrm{Pr}_t/\mathrm{Sc}_t$ | 0.7 | 0.7 | | Tracer | 5% ethylene (passive) | passive scalar (D3Q7 / RRBGK) | | Fluid velocity set / operator | - | D3Q27 / RRBGK | | LES model | dynamic Smagorinsky-Lilly | Smagorinsky $C_S = 0.12$ (provisional) | | Ground wall model | - | IBM EqLog + Monin-Obukhov stability | | Inflow | Vortex Method (mean T only) | SEM + z-varying mean-T inlet | | Refinement | - | static level-2 slab over the building | ## Validation targets All quantities are plot-only in the paper and must be digitized (see `reference/README.md`). The primary targets for Case 2: - **Fig. 5** - inlet profiles ($u$, $k$, $T$) vs TPU Database 2006 (`inlet_profile`). - **Fig. 7** - vertical lines a, b, c behind the building at $x/H = 0.375, 0.625, 1.0$: $\langle u \rangle / u_H$ and $\langle c \rangle / c_0$ with $\pm 15\%$ bars (`behind_building_lines`). - **Fig. 8** - streamlines and mean contours on the symmetry plane (`symmetry_plane` + `full_stats`). - **Fig. 9** - recirculation length vs Ri (shrinks ~32% from Ri 0 to $-1.5$) (`full_stats` mean velocity; ladder). - **Fig. 10** - vertical velocity; **Fig. 11** - $u'w' / u_H^2$ (`symmetry_plane` + `full_stats` 2nd order). - **Figs. 12-13** - power spectral densities at points A-E (`probe_points`). - Flux decomposition ($Q_a \approx 4\, Q_t$ in the recirculation at $\mathrm{Ri} = -1.5$) (`full_stats`). ## Validation ladder and composition matrix Like `05_stratified_street_canyon`, this case is the **top (application-representative) rung** of the stratified-ABL ladder: buoyant Boussinesq scalar + Monin-Obukhov ground wall model + z-varying scalar inlet + voxelized building + passive tracer + SEM + LES + 2:1 refinement, all at once. The `!unroll` Ri ladder additionally sweeps stability (Ri = 0 through -1.5); the $\mathrm{Ri} = 0$ (C1) rung is the in-case neutral point but is **not** a substitute for the standalone neutral-limit regression (it still runs the full building geometry). The lower rungs it depends on: - **Neutral-limit regression** - `07_stratified_neutral_limit`. - **Wall-model differential sign check** - `examples/mo_stability_validation` (GPU-validated, #1046). - **Analytical rungs** (buoyant laminar channel; MO log-law vs analytical $\psi_m/\psi_h$) - NOT yet in the suite; tracked for P5. Composition coverage of *this* case: ``` | single-block | multiblock | +LES | +scalar | +IBM | 2D neutral-limit regression | reg | reg | reg | reg | - | - this case (06, app-rep) | - | X | X | X | X | - ``` Known gaps to fill at P5 (epic #1034, #1039): a single-block feature-alone case, an analytical rung, and a 2D variant. As with case 05, all composition axes are stacked simultaneously, so this case cannot localise a failure to a single interaction - that is what the lower rungs are for. The committed config is full-resolution (level-2 slab); the reduced-domain / level-1 smoke did not exercise the committed level-2 interface. ## Reference and acceptance The reference is the LES of {footcite:t}`zhou2021large`, with the TPU Database 2006 wind tunnel backing Cases 1 and 2 only. There is no field data. Acceptance criteria, stated up front (finalised with `nassu-theory` at P5 where a paper-specific band is needed): - **Dispersion** ($\langle c\rangle / c_0$, Fig. 7 lines a/b/c): CWE quality bands (COST Action 732 / VDI 3783 Part 9) - $\mathrm{FAC2} \geq 0.5$, $\mathrm{NMSE} < 4$, hit rate $q \geq 0.66$ - with the paper's $\pm 15\%$ bands on the behind-building lines. - **Recirculation length vs Ri** (Fig. 9): the leeward recirculation length must shrink monotonically with instability, reproducing the ~32% reduction from $\mathrm{Ri} = 0$ to $-1.5$ to within $\pm 10\%$ of the LES curve. - **Second-order** ($u'w'/u_H^2$, Fig. 11) profiles within the CWE bands on the symmetry plane; flux decomposition sign and ~4:1 advection/turbulent ratio at $\mathrm{Ri} = -1.5$ reproduced. - **Interface continuity (multiblock)**: mean temperature/buoyancy continuous across the level-2 interface (no per-block sawtooth) to the solver-noise floor. - All criteria are evaluated on **time-averaged statistics**, not instantaneous fields (GPU non-determinism, ~1e-6 float32). ## Results ```{note} The integrated stack has been proven to run to completion on GPU and stay finite (a short smoke), but no quantitative results are claimed yet. The comparison notebook (inlet profiles, behind-building lines, recirculation length, $u'w'$, PSDs and the flux decomposition against the digitized Zhou / TPU data) is populated once the digitized reference data and a statistically-converged full-resolution run exist (epic #1034 P5, #1039). ``` ```{toctree} --- hidden: --- 06_stratified_building.ipynb ``` ```{footbibliography} ```