# Mesh Generation

> >

- **Type:** Skill
- **Install:** `agentstack add skill-heshamfs-materials-simulation-skills-mesh-generation`
- **Verified:** Pending review
- **Seller:** [HeshamFS](https://agentstack.voostack.com/s/heshamfs)
- **Installs:** 0
- **Category:** [AI & ML](https://agentstack.voostack.com/c/ai-and-ml)
- **Latest version:** 0.1.0
- **License:** Apache-2.0
- **Upstream author:** [HeshamFS](https://github.com/HeshamFS)
- **Source:** https://github.com/HeshamFS/materials-simulation-skills/tree/main/skills/core-numerical/mesh-generation

## Install

```sh
agentstack add skill-heshamfs-materials-simulation-skills-mesh-generation
```

Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent.

## About

# Mesh Generation

## Goal

Provide a consistent workflow for selecting mesh resolution and checking mesh quality for PDE simulations.

## Requirements

- Python 3.10+
- No external dependencies (uses stdlib)

## Inputs to Gather

| Input | Description | Example |
|-------|-------------|---------|
| Domain size | Physical dimensions | `1.0 × 1.0 m` |
| Feature size | Smallest feature to resolve | `0.01 m` |
| Points per feature | Resolution requirement | `10 points` |
| Aspect ratio limit | Maximum dx/dy ratio | `5:1` |
| Quality threshold | Skewness limit | ` must be a finite positive number, got ...` | `dx`/`dy`/`dz` not finite or not positive | Use a finite positive value |
| ` exceeds maximum (...), got ...` | Input above the resource-exhaustion bound | Use a smaller value |

## Interpretation Guidance

### Aspect Ratio

| Aspect Ratio | Quality | Impact |
|--------------|---------|--------|
| 1:1 | Excellent | Optimal accuracy |
| 1:1 - 3:1 | Good | Acceptable |
| 3:1 - 5:1 | Fair | May affect accuracy |
| > 5:1 | Poor | Solver issues likely |

### Skewness

Skewness is the angular deviation from the ideal cell shape
(`max(|90° - θ_i|) / 90°` for quads/hexes — see `references/quality_metrics.md`).
`mesh_quality.py` works from axis-aligned edge spacings, which describe
orthogonal Cartesian cells whose interior angles are all exactly 90°; it
therefore always reports `skewness = 0.0` for these cells. The thresholds below
apply when a genuine skewness value is obtained from real cell-corner geometry
(e.g. from an unstructured mesh), not from `dx/dy/dz` spacings.

| Skewness | Quality | Impact |
|----------|---------|--------|
| 0 - 0.25 | Excellent | Optimal |
| 0.25 - 0.50 | Good | Acceptable |
| 0.50 - 0.80 | Fair | May affect accuracy |
| > 0.80 | Poor | Likely problems |

> Note: cell elongation is **not** skewness. An anisotropic but orthogonal cell
> (e.g. a wall-aligned boundary-layer cell) has high `aspect_ratio` /
> `size_anisotropy` but zero skewness, and is often perfectly acceptable.

### Resolution Guidelines

| Application | Points per Feature |
|-------------|-------------------|
| Phase-field interface | 5-10 |
| Boundary layer | 10-20 |
| Shock | 3-5 (with capturing) |
| Wave propagation | 10-20 per wavelength |
| Smooth gradients | 5-10 |

## Verification checklist

- [ ] Recorded `dx` and `counts` from `grid_sizing.py --json` and confirmed the smallest physical feature gets enough points (interface ≥5×dx, boundary layer ≥10×dx, wavelength ≥20×dx per Resolution Selection above).
- [ ] For an anisotropic domain, ran `grid_sizing.py` once per differing edge length (or applied `--dx` per axis) — did NOT apply a single `--length`-derived count to unequal edges.
- [ ] Checked the `notes` field for "Grid does not fully cover length" and resolved any partial-coverage warning before trusting `counts`.
- [ ] Logged `aspect_ratio` and `quality_flags` from `mesh_quality.py --json`; confirmed `high_aspect_ratio` is absent OR that the elongation is intentional and physics-aligned (e.g. wall-aligned boundary-layer cell with AR≤100 along the wall).
- [ ] Confirmed the reported `skewness = 0.0` is the expected orthogonal-Cartesian result, NOT a measured quality pass — for unstructured/non-orthogonal cells, obtained a real angle-based skewness from cell-corner geometry and checked it against the <0.8 threshold.
- [ ] Verified `dx` also satisfies the solver's stability constraint (cross-check with numerical-stability) before committing to the resolution.
- [ ] Ran a mesh convergence study (≥3 successively refined grids) and confirmed the quantity of interest changes monotonically/asymptotically before declaring the mesh adequate.

## Common pitfalls & rationalizations

| Tempting shortcut | Why it's wrong / what to do |
|-------------------|------------------------------|
| "`skewness` came back 0.0, so the mesh quality is fine." | `mesh_quality.py` always returns `skewness = 0.0` for axis-aligned spacings — it is a definitional property of orthogonal cells, not a measurement. Real skewness needs cell-corner angles from an unstructured mesh; don't read 0.0 as a passing quality check. |
| "Two grids gave nearly the same answer, so the mesh is converged." | Two grids cannot establish the observed order or the asymptotic range. Use ≥3 successively refined grids and confirm the quantity of interest is converging before quoting any result as mesh-independent. |
| "High `aspect_ratio` was flagged, so the cell is bad." | Elongation is not skewness. A wall-aligned boundary-layer cell with AR up to ~100 is acceptable when aligned with the flow/field; check `size_anisotropy` and the physics, not just the `high_aspect_ratio` flag. |
| "I'll set one `--length` and reuse the `counts` for all axes." | `grid_sizing.py` is isotropic per call — it applies the single derived count to every dimension. For unequal edges this over/under-resolves axes; run it per edge length or supply `--dx` per axis. |
| "`dx = length/resolution` resolves my feature because resolution is large." | Points-per-domain is not points-per-feature. A fine global `dx` can still place too few cells across a thin interface/layer; check `feature_size / dx` against the Resolution Guidelines (5-10 for interfaces, 10-20 for boundary layers). |
| "The mesh is fine enough, so I can ignore the time step." | Mesh resolution and temporal stability are coupled: shrinking `dx` tightens explicit CFL/diffusion limits. A refined mesh that violates the solver's stability constraint diverges — re-check `dt` against numerical-stability after any refinement. |

## Security

### Input Validation
- All inputs (`length`, `resolution`, `dx`, `dy`, `dz`) are validated as finite positive numbers with upper bounds to prevent resource exhaustion
- `dims` is restricted to `{1, 2, 3}`
- `argparse` type parameters reject non-numeric input at the CLI boundary before any processing occurs

### File Access
- Scripts read no external files; all inputs are provided via CLI arguments
- Scripts write only to stdout (JSON output); no files are created unless the agent explicitly uses the Write tool

### Tool Restrictions
- **Read**: Used to inspect script source, references, and user configuration files
- **Write**: Used to save grid sizing results or mesh quality reports; writes are scoped to the user's working directory
- **Grep/Glob**: Used to locate relevant files and search references
- The skill's `allowed-tools` excludes `Bash` to prevent the agent from executing arbitrary commands when processing user-provided inputs

### Safety Measures
- No `eval()`, `exec()`, or dynamic code generation
- All subprocess calls use explicit argument lists (no `shell=True`)
- Reduced tool surface (no Bash) means the agent should use `Read` and `Write` to prepare inputs and capture outputs rather than constructing shell commands from user text
- All output is deterministic JSON with no shell-interpretable content

## Limitations

- **2D/3D only**: No unstructured mesh generation
- **Quality metrics**: Aspect ratio and size anisotropy from axis-aligned spacings only; skewness is reported as 0 for these orthogonal cells (true angular skewness requires real cell-corner geometry)
- **No mesh generation**: Sizing recommendations only
- **Isotropic per call**: `grid_sizing.py` takes a single `--length` and applies the resulting count to every dimension. For an anisotropic domain (e.g. 10 cm × 5 cm), run it once per differing edge length, or compute `dx` from physics and apply it per axis (e.g. `--length 0.10 --dx 5e-5`, then `--length 0.05 --dx 5e-5`).

## References

- `references/mesh_types.md` - Structured vs unstructured
- `references/quality_metrics.md` - Aspect ratio/skewness thresholds

## Version History

- **v1.2.0** (2026-06-23): Corrected skewness science (orthogonal cells now report skewness 0), added `size_anisotropy`, made `mesh_quality.py --dz` optional (2D cells), fixed grid_sizing off-by-one for resolution-derived counts, surfaced dx-override note, corrected output/error-handling docs
- **v1.1.0** (2024-12-24): Enhanced documentation, decision guidance, examples
- **v1.0.0**: Initial release with 2 mesh quality scripts

## Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

- **Author:** [HeshamFS](https://github.com/HeshamFS)
- **Source:** [HeshamFS/materials-simulation-skills](https://github.com/HeshamFS/materials-simulation-skills)
- **License:** Apache-2.0

Install and usage instructions live in the source repository linked above.

## Pricing

- **Free** — Free

## Security capabilities

Automated source analysis of v0.1.0 — what this tool can access:

- **Network access:** no
- **Filesystem access:** no
- **Shell / process execution:** yes
- **Environment & secrets:** no
- **Dynamic code execution:** yes

*"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.*


## Versions

- **0.1.0** — security scan: flagged — Imported from the upstream source.

## Links

- Listing page: https://agentstack.voostack.com/l/skill-heshamfs-materials-simulation-skills-mesh-generation
- Seller: https://agentstack.voostack.com/s/heshamfs
- Browse the marketplace: https://agentstack.voostack.com/browse

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