CFL number

The Courant-Friedrichs-Lewy number ( CFL number or Courant number ) is used in numerical flow simulation for the discretization of time-dependent partial differential equations .

It indicates the maximum number of cells by which a size can move per time step:

${\displaystyle c={\frac {u\cdot \Delta t}{\Delta x}}}$

Thereby is the Courant number, the speed, the discrete time step and the discrete local step. This is motivated by the CFL condition, which states that the explicit Euler method can only be stable for . Similar conditions also apply to other discretization schemes. ${\displaystyle c}$ ${\displaystyle u}$ ${\displaystyle \Delta t}$ ${\displaystyle \Delta x}$ ${\displaystyle c<1}$

The Courant number is named after the mathematicians Richard Courant , Kurt Friedrichs and Hans Lewy , who defined it in 1928.

literature

• Richard Courant, Kurt Friedrichs, Hans Lewy: About the partial difference equations of mathematical physics. In: Mathematische Annalen , Vol. 100 (1928), pp. 32-74, Online , ISSN  0025-5831 .