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)