mesh-generation（网格生成）

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

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

Script Outputs (JSON Fields)

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: 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

# 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

Interpretation Guidance

Aspect Ratio

Skewness

Resolution Guidelines

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: 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