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mesh-generation

@HeshamFS/materials-simulation-skills
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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.

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SKILL.md

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.
allowed-tools Read, Bash, Write, Grep, Glob

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

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