What is Courant Fort?

The Courant–Friedrichs–Lewy (CFL) condition is a condition for the stability of numerical methods that solve time-dependent partial differential equations (PDEs). It arises when discretizing the PDE; in particular, it is relevant for explicit time-stepping schemes. The CFL condition states that the distance that any information travels during the timestep length within the mesh must be lower than the distance between mesh elements. In other words, information from a given cell or mesh element at a given time step must only influence its immediate neighbors in the next time step. Violating the CFL condition in explicit time integration schemes typically leads to unstable simulations, where errors grow rapidly and the solution becomes meaningless.