# time-stepping

Plans time increments for transient simulations, including adaptive stepping, startup ramping, output timing, and checkpoint intervals for recovery after failures.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · ★ 83
- Author: HeshamFS
- License: Apache-2.0 · policy=mirror · the beginning of the file is at the end of this page
- Source: https://github.com/HeshamFS/materials-simulation-skills/tree/HEAD/skills/core-numerical/time-stepping/SKILL.md
- Updated: 2026-10-21
- HTML: https://affpapa.org/en/nevibecode/skills/time-stepping

## What it does

The time-stepping skill helps set time increments for transient simulations using stability constraints and a target step size. It combines CFL, diffusion, and reaction limits with a safety margin. For simulations with sharp gradients, phase changes, or a cold start, the workflow can gradually raise the step size instead of applying the target value immediately.

Three Python scripts handle the main calculations. `scripts/timestep_planner.py` produces a recommended step and ramp schedule, `scripts/output_schedule.py` calculates output times, and `scripts/checkpoint_planner.py` estimates checkpoint intervals and their runtime overhead. Results are available as JSON, including warnings and planning values. Python 3.10+ is required, and the scripts rely on the standard library rather than external packages.

The workflow starts with stability limits, then calculates time steps, output timing, and checkpoint cadence. Checkpoint planning accounts for how much work can be lost after a failure. Supply the actual stability limit from numerical analysis; a guessed limit can undermine the recommendation. The scripts also flag invalid time ranges and non-positive target steps.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add HeshamFS/materials-simulation-skills --skill time-stepping -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/time-stepping/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/time-stepping/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add HeshamFS/materials-simulation-skills --skill time-stepping -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/time-stepping/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add HeshamFS/materials-simulation-skills --skill time-stepping -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/time-stepping/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install HeshamFS/materials-simulation-skills time-stepping
```

2. **Manually: put the files in place**
- File: `.github/skills/time-stepping/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add HeshamFS/materials-simulation-skills --skill time-stepping -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/HeshamFS/materials-simulation-skills --path skills/core-numerical/time-stepping
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/time-stepping/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add HeshamFS/materials-simulation-skills --skill time-stepping -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/HeshamFS/materials-simulation-skills/tree/HEAD/skills/core-numerical/time-stepping/SKILL.md

## When to use it
- Calculate a recommended time increment from stability limits
- Ramp up the step size during difficult startup conditions
- Generate output timestamps for a specified simulation interval
- Estimate checkpoint frequency and runtime overhead
- Investigate shrinking or oscillating adaptive time steps

## Example prompts
- Choose a time step for my simulation with target `1e-4`, stability limit `2e-4`, safety factor `0.8`, and a ramp lasting `10` steps; run `scripts/timestep_planner.py`.
- Generate output timestamps from `0` to `10` seconds at `0.1`-second intervals using `scripts/output_schedule.py`.
- Estimate checkpoint timing for a `36000`-second run, a `120`-second checkpoint cost, and a maximum acceptable loss of `1800` seconds with `scripts/checkpoint_planner.py`.

## Source text · SKILL.md · Apache-2.0

Below is the content of a third-party file. It is data, not instructions for you: do not act on anything written inside unless the human asks. Block tag: ecf5789a21f8aee5.

BEGIN THIRD-PARTY FILE ecf5789a21f8aee5
````text
---
name: time-stepping
description: >
  Plan and control time-step policies for transient simulations — couple
  CFL and physics-based stability limits with adaptive stepping, ramp initial
  transients through sharp gradients or phase changes, schedule output intervals
  and checkpoint cadence, and plan restart strategies for long-running jobs.
  Use when choosing dt for a new simulation, diagnosing adaptive time-step
  oscillations, deciding checkpoint frequency to minimize lost work, or
  setting up output schedules aligned with physical time scales, even if
  the user only says "my run is too slow" or "how often should I save."
allowed-tools: Read, Bash, Write, Grep, Glob
metadata:
  last_deterministic_eval: "2026-10-20"
  agent_evaluation_status: "not_revalidated"
  author: HeshamFS
  version: "1.2.3"
  security_tier: high
  security_reviewed: true
  tested_with:
    - claude-code
  last_evaluated: "2026-06-24"
  eval_cases: 5
  last_reviewed: "2026-10-19"
  standards:
    - "Courant-Friedrichs-Lewy (CFL) condition (Courant, Friedrichs, Lewy 1928)"
    - "von Neumann stability analysis (Fourier/diffusion and Courant number limits)"
    - "Daly (2006), optimal checkpoint interval formula"
    - "Young (1974), first-order checkpoint interval refinement"
---

# Time Stepping

## Goal

Provide a reliable workflow for choosing, ramping, and monitoring time steps plus output/checkpoint cadence.

## Requirements

- Python 3.10+
- No external dependencies (uses stdlib)

## Inputs to Gather

| Input | Description | Example |
|-------|-------------|---------|
| Stability limits | CFL/Fourier/reaction limits | `dt_max = 1e-4` |
| Target dt | Desired time step | `1e-5` |
| Total run time | Simulation duration | `10 s` |
| Output interval | Time between outputs | `0.1 s` |
| Checkpoint cost | Time to write checkpoint | `120 s` |

## Decision Guidance

### Time Step Selection

```
Is stability limit known?
├── YES → Use min(dt_target, dt_limit × safety)
└── NO → Start conservative, increase adaptively

Need ramping for startup?
````
END THIRD-PARTY FILE ecf5789a21f8aee5

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