mesh-generation

# Mesh Generation ## Goal Provide a consistent workflow for selecting mesh resolution and checking mesh quality for PDE simulations. ## Requirements - Python 3.8+ - 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 | `< 0.8` | ## Decision Guidance ### Resolution Selection ``` What is the smallest feature size? ├── Interface width → dx ≤ width / 5 ├── Boundary layer → dx ≤ layer_thickness / 10 ├── Wave length → dx ≤ lambda / 20 └── Diffusion length → dx ≤ sqrt(D × dt) / 2 ``` ### Mesh Type Selection | Problem | Recommended Mesh | |---------|------------------| | Simple geometry, uniform | Structured Cartesian | | Complex geometry | Unstructured triangular/tetrahedral | | Boundary layers | Hybrid (structured near walls) | | Adaptive refinement | Quadtree/Octree or AMR | ## Script Outputs (JSON Fields) | Script | Key Outputs | |--------|-------------| | `scripts/grid_sizing.py` | `dx`, `nx`, `ny`, `nz`, `notes` | | `scripts/mesh_quality.py` | `aspect_ratio`, `skewness`, `quality_flags` | ## Workflow 1. **Estimate resolution** - From physics scales 2. **Compute grid sizing** - Run `scripts/grid_sizing.py` 3. **Check quality metrics** - Run `scripts/mesh_quality.py` 4. **Adjust if needed** - Fix aspect ratios, reduce skewness 5. **Validate** - Mesh convergence study ## Conversational Workflow Example **User**: I need to mesh a 1mm × 1mm domain for a phase-field simulation with interface width of 10 μm. **Agent workflow**: 1. Compute grid sizing: ```bash python3 scripts/grid_sizing.py --length 0.001 --resolution 200 --json ``` 2. Verify interface is resolved: dx = 5 μm, interface width = 10 μm → 2 points per interface width. 3. Recommend: Increase to 500 points (dx = 2 μm) for 5 points across interface. ## Pre-Mesh Checklist - [ ] Define target resolution per feature/interface - [ ] Ensure dx meets stability constraints (see numerical-stability) - [ ] Check aspect ratio < limit (typically 5:1) - [ ] Check skewness < threshold (typically 0.8) - [ ] Validate mesh convergence with refinement study ## CLI Examples ```bash # Compute grid sizing for 1D domain python3 scripts/grid_sizing.py --length 1.0 --resolution 200 --json # Check mesh quality python3 scripts/mesh_quality.py --dx 1.0 --dy 0.5 --dz 0.5 --json # High aspect ratio check python3 scripts/mesh_quality.py --dx 1.0 --dy 0.1 --json ``` ## Error Handling | Error | Cause | Resolution | |-------|-------|------------| | `length must be positive` | Invalid domain size | Use positive value | | `resolution must be > 1` | Insufficient points | Use at least 2 | | `dx, dy must be positive` | Invalid spacing | Use positive values | ## 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 | 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 | ### 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 | ## Limitations - **2D/3D only**: No unstructured mesh generation - **Quality metrics**: Basic aspect ratio and skewness only - **No mesh generation**: Sizing recommendations only ## References - `references/mesh_types.md` - Structured vs unstructured - `references/quality_metrics.md` - Aspect ratio/skewness thresholds ## Version History - **v1.1.0** (2024-12-24): Enhanced documentation, decision guidance, examples - **v1.0.0**: Initial release with 2 mesh quality scripts