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

• Estimate resolution - From physics scales

• Compute grid sizing - Run scripts/grid_sizing.py

• Check quality metrics - Run scripts/mesh_quality.py

• Adjust if needed - Fix aspect ratios, reduce skewness

• 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:

• Compute grid sizing: python3 scripts/grid_sizing.py --length 0.001 --resolution 200 --json

• Verify interface is resolved: dx = 5 μm, interface width = 10 μm → 2 points per interface width.

• 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