The Courant number is used in numerical flow simulation for the discretisation of time-dependent partial differential equations:

Where c₀ is the Courant number, v is the velocity, Δ 𝑡 is the discrete time step and L is the longest element in the direction of flow.

Since the upper limit for L is already given by the Peclet number and is usually relatively small, the time increment Δ 𝑡 must also be chosen to be correspondingly small depending on the speed in order to fulfil the Courant criterion.

The next figure shows the influence of the Courant number on the calculated concentration distribution with otherwise identical model parameters:

Dependence between Courant criterion and numerical dispersion (König, 1991)