Periodic 2D Taylor–Green AMR campaign (prepared, not GPU-qualified)

This validation harness complements DFG Re100 and Jet/body tests. It measures smooth 2D periodic decay and errors crossing fixed refinement interfaces at Re_L=100 and 1000. It does not certify 3D turbulence, LES, Jet performance, wall conditions, dynamic refinement or general high-Re flows.

Reference and conventions

Primary implementation-author documentation, checked 2026-10-18:

TensorMesh, exact velocity and pressure with a consistent phase: https://docs.tensor-mesh.com/example_gallery/fluid/taylor_green.html
AeroSim Nassu, 2D decay, energy and lattice-length Re definition: https://docs.aerosim.io/nassu/validation/analytical/04_taylor_green_vortex_2d/README.html

We use the TensorMesh phase, rescaled to length L=N root cells:

k = 2*pi/L; A(t) = U*exp(-2*nu*k*k*t)
ux = -A*cos(k*x)*sin(k*y)
uy =  A*sin(k*x)*cos(k*y)
p/rho0 = -A*A/4 * (cos(2*k*x)+cos(2*k*y))
E = <|u|^2>/2 = U*U/4 * exp(-4*nu*k*k*t)

Pressure is kinematic, with rho0=1. A global velocity sign reversal leaves pressure unchanged; exchanging sine/cosine without the corresponding pressure phase can reverse its sign. CPU tests independently check momentum residuals. The nonlinear acceleration is a pressure gradient, not zero; the AeroSim page's prose calling advection zero is not adopted. Do not mix phase variants from different references. The formulas above are verified by substitution, not by trusting a copied pressure expression.

Re_L=UL/nu, not Re_k=U/(nuk)=Re_L/(2pi). U=.03 in lattice units, Ma=U/cs=.0519615, cs^2=1/3, nu_root=.03N/Re_L. Acoustic refinement uses h_l=dt_l=2^-l: lattice velocity stays U, nu_l=2^lnu_root and tau_l=.5+3nu_l. The worst root tau is .50288 (N32/Re1000), omega=1.98855, inside the existing config guard. No viscosity clamping or guard override.

All initial arrays are physical FP64 equilibrium populations, supplied to the public shifted-FP32 postcollision-G initializer. rho=1+3p at each true cell center. These are valid equilibrium postcollision states, but do not include Chapman–Enskog nonequilibrium stress; startup acoustic/kinetic error remains in the measurements and is shared with uniform baselines. The incompressible reference is not an exact finite-Mach LBM solution. This is why resolution alone need not remove the full error floor.

Geometry and workload

All patches use level-wide union form, so origins are zero, including fine arrays with holes. Coordinates are (index+.5)*2^-level. Metrics integrate only ACTIVE leaves, each weighted by 4^-level. Covered cells and halo cells never enter norms or mass. Geometry tests prove exact single coverage at root-cell resolution. All blocks are 8x8, and both root dimensions are periodic.

At each root N=32,64:

2 levels: L1 rectangle (N/8,N/8,7N/8,3N/4), in L0 indices.
3 levels: same L1 plus L2 rectangle (3N/4,N/2,3N/2,5N/4), in L1 indices.

These off-axis boundaries cross nonzero flow and gradients rather than sitting only on symmetry or stagnation lines. Whole geometry scales with N.

16 cases: at each Re, uniform N=32,64,128,256 plus AMR (root32/root64)x(depth2/depth3). Each AMR case therefore has both a same-root uniform baseline and a uniform baseline at its finest spacing. Uniform N is its own lattice length, so nu and step count are scaled to represent the same nondimensional solution. Samples t*=tU/L = 0,.12,.24,.36,.48. End time is 16*N base steps, a meaningful .48 domain turnover or 3.016 vortex-scale turnover times (scale 1/k). At Re1000 energy decays about 7.3%; at Re100 about 53.1%. No plots or full fields; each case writes five diagnostic rows and provenance, incrementally.

Running (GPU owner must schedule launches)

CPU checks, from the repository root:

PYTHONPATH=src python -m unittest discover -s tests/validation/taylor_green -p 'test_*.py' -v

One GPU case, on the scheduled worker after checking occupancy:

CUDA_VISIBLE_DEVICES=<physical-id> python tests/validation/taylor_green/run_case.py --repo /path/to/reviewed/checkout --re 100 --n 32 --depth 1 --output output/taylor_green/re100_n32_d1.json

Depth 1 is uniform. Run uniform cases before AMR for each Re; inspect baseline screening failures before proceeding. For a complete matrix, repeat the uniform call with N=32,64,128,256 and AMR calls with N=32,64 / depth=2,3, at each Re. Use serial process startup on the parent's assigned Horsea GPUs. This harness does not schedule or acquire GPUs. No GPU was used during preparation.

python tests/validation/taylor_green/assess.py output/taylor_green/re*_n*_d*.json --output output/taylor_green/assessment.json

The local API/geometry review used clean staging commit cd3a657f9d. This is not a claim of results on d79 or any historical commit. Each runtime output records actual Git HEAD/dirty state, an aggregate source-tree hash, plus SHA256 of all harness Python files. Assessment refuses dirty checkouts and mixed source or harness identities. Keep reports outside the checkout or .gitignore them so new outputs do not change its dirty flag between cases. The source-tree hash excludes bytecode caches; production qualification requires a clean checkout. The runner uses the existing PeriodicBlockStepper / FixedPatchStepper periodic paths only. It does not depend on the new channel-root implementation.

Preregistered assessment, before any GPU results

All sampled times must satisfy finite screening ceilings:

Relative composite velocity L2 <= 5%
Relative globally gauge-adjusted pressure L2 <= 15%
Relative kinetic-energy error <= 5%
Composite mass drift from downloaded t0 <= 1e-5

These are screening budgets, not literature-certified tolerances. Acceptance also requires all 16 cases, common source/harness, correct nondimensional times and viscosity, and baseline-relative checks on worst post-startup-sample errors:

AMR error <= max(2 * same-root uniform error, declared numerical floor).
Root64 AMR error <= max(.9 * root32 AMR error, floor), for each depth/Re.
Uniform256 error <= max(.9 * uniform32 error, floor).

Floors: velocity .002, pressure .02, energy .004. They are declared low-Mach / equilibrium-startup budgets, not fitted to observed results. Ma^2=.0027 motivates their scale; it is an asymptotic expectation, not a proof of those coefficients. The coarse baseline sets the AMR budget because much of the domain remains coarse. The finest uniform error and AMR/fine ratio are always reported, with no claim that partial refinement should match a fully fine domain. A pass below a floor is bounded accuracy, not a measured convergence order. Report errors and ratios even for a pass. Failure requires diagnosis or a separately preregistered follow-up, never retroactive tolerance tuning. Higher Re is deliberately absent; Re100/1000 must first be stable, resolved and reviewed.

Diagnostics use one global pressure gauge, direct cell-center analytic values, kinetic energy per unit reference mass, and actual leaf cell areas. Composite midpoint quadrature introduces a small initial energy integration error, retained rather than subtracted. Mass drift is relative to downloaded t0, so density initialization and mixed-grid quadrature do not masquerade as time drift.

Pilot scheduling and transfer-consistency scope

Start with one uniform case and one matched AMR case; the 16-case matrix is a qualification plan, not authorization to launch every case automatically. The GPU owner reviews the pilot before expanding it. Each process prints a flushed READY only after initialization, a real base step exercising every level's kernel/halo/transfer path, and a finite positive-density download check. That step belongs to the measured trajectory; it is not discarded warmup. PROGRESS messages contain each of the five diagnostic samples. READY alone is not an accuracy pass. Reports include per-level active cells, hops and collision updates.

The complete matrix costs 768,540,672 active collision updates and 21,504 root intervals, excluding ghost streaming, halos, transfers and diagnostic work. Uniform N256 is the largest case (268,435,456 updates / 4096 intervals per Re). AMR N64/depth3 needs 50,987,008 updates / 1024 intervals. These are work counts, not GPU wall-time estimates. Baseline comparisons remain available on failed screens and partial pilots; absent/nonfinite operands are null, never passing.

Acoustic viscosity scaling and unchanged lattice velocity do not by themselves prove nonequilibrium-stress consistency across refinement interfaces. A smooth collocated Chapman–Enskog postcollision nonequilibrium has a (tau-1)*h factor; the existing implementation instead uses volumetric piecewise-constant explosion and stream-only ghosts. Whether that actual transfer construction achieves the needed stress accuracy is an unresolved question for this pilot to measure. It is not a proven defect, and a collocated-state scaling factor must not be inserted into this different transfer operator without a separate derivation and validation. This campaign measures the current operator and makes no theoretical stress-consistency certification or production-kernel change.

Repository integration

The four Python harness files remain together under tests/validation/taylor_green, so runtime provenance hashes precisely this harness directory. Formatting changes produce a new harness identity; preparation and integrated receipts must not be mixed. All analytic definitions, numerical floors, assessment gates, sample times, and source-import assertions are unchanged. Production source is unchanged from the cd3 snapshot; these periodic tests do not waive the separate channel GPU gate.

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