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

• Get stability limits - Use numerical-stability skill

• Plan time stepping - Run scripts/timestep_planner.py

• Schedule outputs - Run scripts/output_schedule.py

• Plan checkpoints - Run scripts/checkpoint_planner.py

• 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:

• Plan checkpoints based on acceptable lost work: python3 scripts/checkpoint_planner.py --run-time 36000 --checkpoint-cost 120 --max-lost-time 1800 --json

• 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