Example: adaptive_time_stepping_demo
Figure 4.3 — Example: Adaptive Time Stepping Demo
Crate: cfd-suite (workspace root)
Run: cargo run --example adaptive_time_stepping_demo
Source: examples/adaptive_time_stepping_demo.rs
What This Example Demonstrates
Three adaptive time-step strategies applied to the test ODE dy/dt = −2y (exact: y(t) = exp(−2t)), showing accuracy and efficiency tradeoffs.
| Strategy | API | Basis |
|---|---|---|
| CFL-based | AdaptationStrategy::Cfl | Stability: Δt ≤ CFL·min(Δx/ |
| Error-based | AdaptationStrategy::Error | Richardson extrapolation |
| Combined | AdaptationStrategy::Combined | min(CFL-limited, error-controlled) |
Key Code Snippet
use cfd_2d::schemes::time::{
AdaptationStrategy, AdaptiveController, AdaptiveTimeIntegrator, StateVector,
};
let y0 = StateVector::from_shape_vec([1], vec![1.0])?;
// CFL strategy: stable for advection-dominated problems
demonstrate_cfl_adaptation(&y0, t_final)?;
// Error strategy: targets local truncation error ε ≤ ε_target
demonstrate_error_adaptation(&y0, t_final)?;
// Combined: safest for production simulations
demonstrate_combined_adaptation(&y0, t_final)?;Physics Background
For explicit schemes, CFL condition bounds the time step:
CFL = |u| · Δt / Δx ≤ CFL_max
CFL > 1 causes the numerical domain of dependence to exceed the physical one, leading to instability. Richardson extrapolation estimates the local truncation error by comparing a full step with two half-steps:
ε ≈ |y_full − y_half| / (2^p − 1)
where p is the scheme order.