Agent-Skills.md

Agent Skills: Mesh Generation

Plan and evaluate mesh generation for numerical simulations. Use when choosing grid resolution, checking aspect ratios/skewness, estimating mesh quality constraints, or planning adaptive mesh refinement for PDE discretization.

UncategorizedID: HeshamFS/materials-simulation-skills/mesh-generation

Repository

HeshamFS/materials-simulation-skills
HeshamFSLicense: Apache-2.0
262

Install this agent skill to your local

pnpm dlx add-skill https://github.com/HeshamFS/materials-simulation-skills/tree/HEAD/skills/core-numerical/mesh-generation

Skill Files

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skills/core-numerical/mesh-generation/SKILL.md

Skill Metadata

Name
mesh-generation
Description
Plan and evaluate mesh generation for numerical simulations. Use when choosing grid resolution, checking aspect ratios/skewness, estimating mesh quality constraints, or planning adaptive mesh refinement for PDE discretization.

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: 
    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

| 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 |

Security

The mesh-generation scripts enforce the following safeguards:

  • Strict numeric validation: All inputs (length, resolution, dx, dy, dz) are validated as finite positive numbers with upper bounds to prevent resource exhaustion.
  • Dimension constraint: dims is restricted to {1, 2, 3}.
  • Type enforcement: argparse type parameters reject non-numeric input at the CLI boundary before any processing occurs.
  • Reduced tool surface: The skill's allowed-tools excludes Bash to prevent the agent from executing arbitrary commands when processing user-provided inputs. The agent should use Read and Write to prepare inputs and capture outputs rather than constructing shell commands from user text.

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