time-stepping

Adaptive time-stepping combines CFL/physics stability limits with target step sizes and safety margins to automatically adjust dt during runs. This prevents instability from exceeding stability thresholds while respecting computational targets, producing recommended dt values that balance accuracy and performance.

Ramping startup implements linear, geometric, or adaptive growth of initial time steps to smoothly transition from small dt to target dt, reducing shock and numerical noise at simulation onset. This avoids abrupt jumps that destabilize early iterations while maintaining physical accuracy.

Output and checkpoint cadence scheduling precomputes restart readiness by aligning output intervals and checkpoint costs with total run time, minimizing lost work during interruptions. This ensures frequent saves at predictable intervals without excessive I/O overhead.

Yes, this Skill requires only Python 3.8+ with stdlib—no external packages needed. It accepts stability limits, target dt, run time, and output intervals as plain inputs and produces dt recommendations and ramp schedules as JSON output.

CFL constraints apply when coupling explicit methods or convection-dominated physics that require dt ≤ CFL·Δx/velocity. Adaptive stepping enforces these limits dynamically while respecting safety margins, preventing instability from grid-dependent violations.