numerical-stability
Analyze and enforce numerical stability for time-dependent PDE simulations. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.
npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill numerical-stability --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Numerical Stability ## Goal Provide a repeatable checklist and script-driven checks to keep time-dependent simulations stable and defensible. ## Requirements - Python 3.8+ - NumPy (for matrix_condition.py and von_neumann_analyzer.py) - See `scripts/requirements.txt` for dependencies ## Inputs to Gather | Input | Description | Example | |-------|-------------|---------| | Grid spacing `dx` | Spatial discretization | `0.01 m` | | Time step `dt` | Temporal discretization | `1e-4 s` | | Velocity `v` | Advection speed | `1.0 m/s` | | Diffusivity `D` | Thermal/mass diffusivity | `1e-5 m²/s` | | Reaction rate `k` | First-order rate constant | `100 s⁻¹` | | Dimensions | 1D, 2D, or 3D | `2` | | Scheme type | Explicit or implicit | `explicit` | ## Decision Guidance ### Choosing Explicit vs Implicit ``` Is the problem stiff (fast + slow dynamics)? ├── YES → Use implicit or IMEX scheme │ └── Check conditioning with matrix_condition.py └── NO → Is CFL/Fourier satisfied with reasonable dt? ├── YES → Use explicit scheme (cheaper per step) └── NO → Consider implicit or reduce dx ``` ### Stability Limit Quick Reference | Physics | Number | Explicit Limit (1D) | Formula | |---------|--------|-----
- Goal
- Requirements
- Inputs to Gather
- Decision Guidance
- Choosing Explicit vs Implicit
- Stability Limit Quick Reference
- Script Outputs (JSON Fields)
- Workflow
- Conversational Workflow Example
- Pre-Simulation Stability Checklist
- CLI Examples
- Error Handling
- Interpretation Guidance
- Limitations
python3 scripts/cfl_checker.py --dx 0.01 --dt 1e-4 --diffusivity 1e-3 --dimensions 2 --json Check CFL/Fourier for 2D diffusion-advection python3 scripts/cfl_checker.py --dx 0.1 --dt 0.01 --velocity 1.0 --diffusivity 0.1 --dimensions 2 --json Von Neumann analysis for custom 3-point stencil python3 scripts/von_neumann_analyzer.py --coeffs 0.2,0.6,0.2 --dx 1.0 --nk 128 --json Detect stiffness from eigenvalue estimates python3 scripts/stiffness_detector.py --eigs=-1,-1000 --json Check matrix conditioning for implicit system python3 scripts/matrix_condition.py --matrix A.npy --norm 2 --json
What does the numerical-stability skill do?
Analyze and enforce numerical stability for time-dependent PDE simulations. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.
How do I install it?
Run `npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill numerical-stability --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From FreedomIntelligence/OpenClaw-Medical-Skills, a repository with 2,909 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.