The condition is named after Richard Courant, Kurt Friedrichs, and Hans Lewy who described it in their 1928 paper.
[1] The principle behind the condition is that, for example, if a wave is moving across a discrete spatial grid and we want to compute its amplitude at discrete time steps of equal duration,[2] then this duration must be less than the time for the wave to travel to adjacent grid points.
As a corollary, when the grid point separation is reduced, the upper limit for the time step also decreases.
In essence, the numerical domain of dependence of any point in space and time (as determined by initial conditions and the parameters of the approximation scheme) must include the analytical domain of dependence (wherein the initial conditions have an effect on the exact value of the solution at that point) to assure that the scheme can access the information required to form the solution.
To make a reasonably formally precise statement of the condition, it is necessary to define the following quantities: The spatial coordinates and the time are discrete-valued independent variables, which are placed at regular distances called the interval length[3] and the time step, respectively.
Operatively, the CFL condition is commonly prescribed for those terms of the finite-difference approximation of general partial differential equations that model the advection phenomenon.
In the two-dimensional case, the CFL condition becomes with the obvious meanings of the symbols involved.