Time Stepping

Goal

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

Requirements

• Python 3.8+
• 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?
├── YES → Start at dt_init, ramp to dt_target over N steps
└── NO → Use dt_target from start

Ramping Strategy

Problem Type	Ramp Steps	Initial dt
Smooth IC	None needed	Full dt
Sharp gradients	5-10	0.1 × dt
Phase change	10-20	0.01 × dt
Cold start	10-50	0.001 × dt

Script Outputs (JSON Fields)

Script	Key Outputs
scripts/timestep_planner.py	dt_limit, dt_recommended, ramp_schedule
scripts/output_schedule.py	output_times, interval, count
scripts/checkpoint_planner.py	checkpoint_interval, checkpoints, overhead_fraction

Workflow

1. Get stability limits - Use numerical-stability skill
2. Plan time stepping - Run scripts/timestep_planner.py
3. Schedule outputs - Run scripts/output_schedule.py
4. Plan checkpoints - Run scripts/checkpoint_planner.py
5. Monitor during run - Adjust dt if limits change

Conversational Workflow Example

User: I'm running a 10-hour phase-field simulation. How often should I checkpoint?

Agent workflow:

1. Plan checkpoints based on acceptable lost work:

   python3 scripts/checkpoint_planner.py --run-time 36000 --checkpoint-cost 120 --max-lost-time 1800 --json
   

2. Interpret: Checkpoint every 30 minutes, overhead ~0.7%, max 30 min lost work on crash.

Pre-Run Checklist

• Confirm dt limits from stability analysis
• Define ramping strategy for transient startup
• Choose output interval consistent with physics time scales
• Plan checkpoints based on restart risk
• Re-evaluate dt after parameter changes

CLI Examples

# Plan time stepping with ramping
python3 scripts/timestep_planner.py --dt-target 1e-4 --dt-limit 2e-4 --safety 0.8 --ramp-steps 10 --json

# Schedule output times
python3 scripts/output_schedule.py --t-start 0 --t-end 10 --interval 0.1 --json

# Plan checkpoints for long run
python3 scripts/checkpoint_planner.py --run-time 36000 --checkpoint-cost 120 --max-lost-time 1800 --json

Error Handling

Error	Cause	Resolution
dt-target must be positive	Invalid time step	Use positive value
t-end must be > t-start	Invalid time range	Check time bounds
checkpoint-cost must be < run-time	Checkpoint too expensive	Reduce checkpoint size

Interpretation Guidance

dt Behavior

Observation	Meaning	Action
dt stable at target	Good	Continue
dt shrinking	Stability issue	Check CFL, reduce target
dt oscillating	Borderline stability	Add safety factor

Checkpoint Overhead

Overhead	Acceptability
< 1%	Excellent
1-5%	Good
5-10%	Acceptable
> 10%	Too frequent, increase interval

Limitations

• Not adaptive control: Plans static schedules, not runtime adaptation
• Assumes constant physics: If parameters change, re-plan

References

• references/cfl_coupling.md - Combining multiple stability limits
• references/ramping_strategies.md - Startup policies
• references/output_checkpoint_guidelines.md - Cadence rules

Version History

• v1.1.0 (2024-12-24): Enhanced documentation, decision guidance, examples
• v1.0.0: Initial release with 3 planning scripts