Name: Mesh Generation
Author: huamu668

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Mesh Generation | Skills Pool

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

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

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.

# 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

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`

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`

Script	Key Outputs
`scripts/grid_sizing.py`	`dx`, `nx`, `ny`, `nz`, `notes`
`scripts/mesh_quality.py`	`aspect_ratio`, `skewness`, `quality_flags`

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

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

Mesh Generation

Goal

Requirements

Inputs to Gather

Decision Guidance

Mesh Generation

Goal

Requirements

Inputs to Gather

Decision Guidance

Resolution Selection

Mesh Type Selection

Script Outputs (JSON Fields)

Workflow

Conversational Workflow Example

Pre-Mesh Checklist

CLI Examples

Error Handling

Interpretation Guidance

Aspect Ratio

Skewness

Resolution Guidelines

Limitations

References

Version History

Llm Trading Agent Security

Energy Procurement

Council

Carrier Relationship Management

Market Research

Market Research

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

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