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numerical-stability

Maintainer FreedomIntelligence · Last updated April 1, 2026

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.

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Original source

FreedomIntelligence/OpenClaw-Medical-Skills

https://github.com/FreedomIntelligence/OpenClaw-Medical-Skills/tree/main/skills/numerical-stability

Maintainer: FreedomIntelligence
License: MIT
Last updated: April 1, 2026

Skill Snapshot

Key Details From SKILL.md

2 min

Key Notes

Provide a repeatable checklist and script-driven checks to keep time-dependent simulations stable and defensible.
python3 scripts/cfl_checker.py --dx 0.1 --dt 0.01 --velocity 1.0 --diffusivity 0.1 --dimensions 2 --json.

Source Doc

Excerpt From SKILL.md

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`

Stability Limit Quick Reference

Physics	Number	Explicit Limit (1D)	Formula
Advection	CFL	C ≤ 1	`C = v·dt/dx`
Diffusion	Fourier	Fo ≤ 0.5	`Fo = D·dt/dx²`
Reaction	Reaction	R ≤ 1	`R = k·dt`

Multi-dimensional correction: For d dimensions, diffusion limit is Fo ≤ 1/(2d).

Use cases

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.

Not for

Do not rely on this catalog entry alone for installation or maintenance details.

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