Courant number#
Also known as: CFL number.
Named after: Richard Courant (1888-1972).
$$\text{Co} \stackrel{\text{def}}{=} \frac{U t}{L} \sim \frac{\text{distance travelled per step}}{\text{cell length}}$$
Description#
Measures the distance information travels in one time step relative to a cell length. It is a stability and accuracy indicator for time-marching numerical schemes.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| velocity | \(U\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
| time | \(t\) | \(\mathrm{s}\) | \(\text T\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
Regimes#
Explicit time integration
| Range | Regime | Description |
|---|---|---|
| 0 – 1 | subcell advection | Information travels less than one characteristic length per time step. Explicit advection schemes are more likely to remain stable. |
| 1 – ∞ | supercell advection | Information travels more than one characteristic length per time step. Many explicit schemes become unstable or inaccurate unless additional treatment is used. |