13.5.3 Stability

The time step of the first order space convex scheme (Section 13.5.1) must fulfill a CFL (Courant-Friedrichs-Levy) condition [126] so that the scheme is stable. The CFL condition demands that the front must not cross more than one grid cell at each time step. Hence it is required that

$$\max_S F \Delta t \le \Delta x,$$

where $S$ is the domain of $F$ and hence all values of $F$ have to be taken into account [121].