# spheroid_drag

Family 15: steady laminar drag of a spheroid aligned with the flow (OpenFOAM through Studio's external-flow solver).

Anchor: for the sphere (length / diameter = 1) the Schiller-Naumann correlation Cd = 24/Re (1 + 0.15 Re^0.687), good to
a few % below Re 800. Slender or flat spheroids have no simple formula over this range, which is the point of the
space. Cd uses the frontal area and Re the equatorial diameter D. Flow solves carry the velocity-field discretisation
error of Studio's mesh, so the bands here are wider than for the solid families.

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `aspect` | 0.5 - 2.0 |
| `Re` | 2.0 - 150.0 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `cd` | 1.1 % / 2.7 % / 2.7 % | max 0.013 % | max - |

## Checks

- points: 35 solved, 0 failed
- three-mesh studies: 7 (every 5th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0 %
- neighbour check: flagged 1, re-solved on a finer mesh 1, unresolved 0
- direction checks: cd vs Re ok (rho -0.998)

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `cd_over_sn` | 1.026 | 1.143 | 1.179 |
| `cd_studio` | 1.287 | 3.544 | 9.932 |

## Columns of points.csv

parameters, the answers, `<answer>_band` (relative), the hand-theory ratios, `mirror_err`, `equilibrium_err` (where a single reaction exists), `<answer>_loo_err` / `_neighbour_flag` (leave-one-out prediction from all other points), `<answer>_recheck_diff` / `_flag_resolved` (finer re-solve of a flagged point), `has_gci` / `has_similarity` / `has_calculix`, `nodes`, `solve_s`, `studio` (version).

Solved with NovaSolver Studio through the same commands an AI client uses over MCP; the first section says which solver and mesh. The claim is verification (the equations are solved within the band), not validation against tests.

## License

This data is licensed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Credit: NovaSolver, https://novasolver.jp/studio/verified/
Provided as is, without warranty. Design decisions remain the user's responsibility.