Guide 12 · September 20, 2026

Put the next cells around the rings.

The outer-band experiment supports a more targeted next mesh: extend fine coverage around the contracting annulus and its flared axial region. Adding another level only at the center misses most of the source sensitivity sampled here.

This September 20 mesh-design study used Oliver’s outer-band geometry. The run has since completed through t = 0.995 with all 280 native states validated. Current numerical record →

Spatial source sensitivity comes first

We evaluated 54 four-cell-wide patches at t = 0.937, 0.985, and 0.995, using three radial similarity coordinates, three axial coordinates, and two azimuths. Each patch uses h, h/2, and h/4 source evaluations, with fine samples volume-averaged onto the same coarse cells. A fourth evaluation halves the force's time-derivative window. These probes evaluate the prescribed source independently of the evolved trajectory.

The largest sampled force difference between h and h/2 is 50.9% of the h/4 reference RMS, followed by 20.3% between h/2 and h/4. Halving the derivative window changes force by at most 2.1 × 10⁻⁷ in the same relative measure. These are local patch results, not whole-domain error bounds. The window check is not a solver-timestep convergence test.

Values are the RMS directional derivative of the Cartesian force vector, multiplied by the current cell width and divided by local force RMS. They indicate where variation is sharp; they do not estimate the error reduction from anisotropic cells. Radial variation dominates the equatorial example, while axial variation becomes comparable farther up the flare. At the same radius and height, the coordinate-axis and 45° probes can differ by one refinement level because the existing fine regions are cubes.

Measure real boxes before spending memory

A mesh-only AMReX executable uses the production tagger and reproduces every box in Oliver's frozen mesh. It then builds 26 alternatives without allocating flow fields or advancing a timestep. Each build uses less than 29 MiB. Original outer bands and core cubes are retained. Candidate rings include physical buffers and ancestor coverage; AMReX still uses cubic Cartesian cells in a fully three-dimensional solver.

The memory estimates scale Oliver's observed peak by stored-cell count. They are screening estimates, not late-time capacity guarantees. Box count, scratch allocation, and evolving memory demand still require a bounded pilot under the 11.5 GiB RSS guard and 20 GiB free-disk reserve.

The leading low-cost ring is centered near r = 0.108, z = 0 and extends the existing 1/1024 spacing outward. It covers 10 of the 54 source patches at their next finer level. Its heuristic coverage score is 28.8% averaged over the three sampled times, versus 0.047% for another central cube. The score weights squared h-to-h/2 source differences by patch volume, normalizes each time separately, and requires coverage of the entire patch. Overlapping patches are not a domain integral, and the score is not a predicted solution-error reduction. In particular, this ring covers none of the weighted t = 0.937 sample set.

What must happen before another long run

First finish the native discrepancy map and probe its largest differences. Then test the selected geometry with manufactured solutions, interface checks, and a bounded late-time capacity pilot. A short restart can check capacity but cannot establish the accuracy of a different mesh's from-rest history. Temporal refinement must be checked independently. A new accepted trajectory would start from rest with a pinned mesh, forcing, clock, and complete native archive.

These measurements justify a targeted mesh candidate, not a claim of convergence or singularity. Broader time, azimuth, and negative-z sampling may change the ranking. Refining both r and z coverage does not require a curvilinear or axisymmetric solver.

Source hashes, all probe metrics, all 27 mesh costs, and leading candidate geometry · Original derivation and launch record

Reproduce the diagnostic workflow

python -m scripts.export_mesh_snapshot \
  --run outputs/outer-run --exporter build/amrex-omp/ns_volume_export \
  --steps 1847 2627 --output outputs/outer-snapshots
python -m scripts.compare_mesh_snapshots \
  --baseline outputs/kay-snapshots --candidate outputs/outer-snapshots \
  --output outputs/native-comparison
python -m scripts.plan_mesh_sensors \
  --snapshot outputs/outer-snapshots/manifest.json \
  --table outputs/outer-run/profile.tbl --output outputs/source-requests.json
python -m scripts.mesh_source_sensors \
  --executable build/amrex-omp/ns_force_probe \
  --table outputs/outer-run/profile.tbl --requests outputs/source-requests.json \
  --output outputs/source-sensors
cmake --build build/amrex-omp --target ns_mesh_probe
python -m scripts.rank_mesh_candidates \
  --executable build/amrex-omp/ns_mesh_probe \
  --snapshot outputs/outer-snapshots/manifest.json \
  --bands site/data/outer-refinement.bands \
  --sensors outputs/source-sensors/sensors.json --output outputs/mesh-ranking

Use a configured AMReX build and fresh output directories. Select only completed native states with matching clocks. The snapshot exporter verifies original native hashes before and after reading; the comparator rechecks exported bytes, active volume, energy, peak speed, and all six components for finiteness. The cost probe checks its entire baseline box layout against the frozen snapshot.