CFL Condition

Stability condition for explicit time integration.

$ formula: C = \dfrac{u \Delta t}{\Delta x} \le C_{max}

u — wave speed (m/s)Δt — time step (s)Δx — grid spacing (m)C_max (e.g., 1.0 advect, 0.5 RK4)

C (current)

0.1000 ✓ stable

Δt_max for current Δx

5.000e-3 s

Explicit Euler 1-D advection: C_max = 1. Higher-order RK (e.g., RK4) typically allows C ≈ 1.4–2 for advection, but viscous & non-linear terms add tighter limits.

CFL numerics stability